ALBERT

Description: This paper presents the development of an adaptive state estimator and an output controller based on the attractive ellipsoid method (AEM) for a class of uncertain non-linear systems (quasi-Lipschitz with external perturbations). The proposed method guarantees that, under a specific persistent excitation condition, the controlled system trajectories converge to an ellipsoid having a smaller trace of the corresponding inverse ellipsoidal matrix comparing to classical AEM without adaptation. An underactuated vertical double pendulum is considered as an experimental illustrative example of the suggested approach.

Description: In this paper, non-linear time-varying systems with slowly varying parameters are considered. Using slowly varying control Lyapunov function and considering a cost function, a controller (with closed-form structure) is presented which guarantees asymptotic stability of the closed-loop non-linear slowly varying system. Moreover, the Hamilton–Jacobi–Bellman equation is analysed to show that the proposed controller is a sub-optimal controller and the response of the closed-loop system may be very close to its optimal solution. Additionally, in order to show the applicability of the proposed method, it is applied to the time-varying inertia pendulum, which is one of the famous benchmarks among the non-linear time-varying systems. Then, the efficiency of the designed controller is compared with that of a numerical optimal controller, which is called, ‘receding horizon generalization of point-wise min-norm controller’. Simulation results demonstrate the applicability and efficiency of the proposed method.

Description: This paper addresses the problem of designing a static output feedback sliding mode control algorithm for linear MIMO systems with mismatched parameter uncertainties and matched perturbations. Once the system is in the sliding mode, the proposed output-dependent sliding variable can guarantee robust stability of the closed-loop system. The existence condition of the sliding variable is determined by solving the coupled algebraic Riccati equations which are involved with the original system parameters. The developed control law having the min–max property can guarantee that the system states are globally driven to and are finally maintained on the sliding variable in finite time. The high-gain control problem can be effectively avoided. The feasibility of the proposed method is demonstrated by simulation results.

Description: The objective of this paper is to study the notion of regional observability of a distributed parameter system governed by semilinear hyperbolic equations. This original concept is interested in the reconstruction of the state only on a subregion of the boundary of the system evolution domain . We give definition and some properties of this notion and we show that under some hypothesis, the regional boundary observability is guarantied. We use the analytical case by sectorial property of the considered dynamic operator and converted to a fixed point problem, and we show that it is possible to reconstruct such a state on a desired subregion . This approach leads to interesting results which are performed through numerical example and simulations.

Description: This paper deals with the distributed robust output regulation problem for the multi-agent systems with general nonlinear dynamics and uncertainty parameters. Assume that the information of active leaders or environmental disturbances cannot be completely measurable for all other agents. By employing the centre manifold theory and characteristics of the agents’ communication, the nonlinear distributed dynamic feedback controllers are designed to make the agents asymptotically track the references or reject the disturbance signals, which are generated by the exosystem. Two numerical examples are provided to show the effectiveness of the main results.

Description: This paper investigates event-triggered leaderless and leader-following consensus problems of multi-agent systems under jointly connected topology. A state-dependent event condition is proposed for each agent, which only relies on its own state and the last sampled data of itself and its neighbours. Based on the Lyapunov technique and algebraic graph theory, the designed event-triggered control strategies are proved to solve the leaderless and leader-following consensus problems when the topology is jointly connected. Moreover, such strategies can exclude Zeno-behaviour. Simulations illustrate the effectiveness of the theoretical results.

Description: By the theory of Sturm–Liouville eigenvalue problems, it is shown that the stability of one-dimensional wave equations with variable coefficients coupled with an ordinary differential equation (ODE) system on general tree-shaped networks is equivalent to that of its subsystem (called the base system). Thus, it is proved that the coupled system can arrive at asymptotical stability, if, for every interior vertex of the subsystem, the spectra of any two edges joined one common interior vertex of the subsystem are disjoint. Especially, the coupled system with one fixed root is exponentially stable. In the end, a star with three edges and a tree-shaped networks with 10 edges are given to verify the theoretical results.

Description: This paper studies the H consensus problem of multi-agent systems by means of a simultaneous stabilization approach. It is shown that the H consensus design problem for n coupled agents can be equivalently characterized as a problem of the simultaneous H stabilization of n – 1 independent subsystems. A new consensus analysis condition is obtained by investigating the corresponding simultaneous H stabilization problem. Based upon the analysis condition, a necessary and sufficient condition is derived to guarantee the consensus of multi-agent systems with a prescribed H performance, where the controller gain matrix is not coupled with the Lyapunov matrices, but parametrized by a positive-definite matrix. Iterative convex optimization approaches are further developed to solve the synthesis condition and to choose the initial values. Finally, a numerical example is given to show the applicability of the results.

Description: This article is concerned with the controllability of damped second-order impulsive neutral integrodifferential systems with infinite delay in Banach spaces. A set of sufficient conditions for the controllability of such systems are formulated by using a fixed point analysis approach. In particular, the compactness condition on the cosine family of operators appearing in various literatures is not required here. At last, an example is given to illustrate the obtained result.

Description: We consider an approximation scheme using hybrid functions for solving time-delayed optimal control problems with terminal inequality constraints. Using a Páde approximation, the problem is first transformed into one without a time-delayed argument. A computational method based on hybrid functions in time-domain is then proposed for solving the obtained non-delay optimal control problem. Hybrid functions integral operational matrix and direct collocation method are utilized to find the approximated optimal trajectory and the optimal control law of the original problem. Numerical results are also given to demonstrate the efficiency of the method.

Description: This paper investigates the problem of D-stability performance of an L 2 point formation control system with parametric uncertainties. A Quasi linear parameter varying (QLPV) model is introduced for the L 2 point formation flying, based on which a nonlinear control strategy is developed via the polynomial eigenstructure assignment (PEA) approach. The designed controller can guarantee the closed-loop system with invariant performance over a wide range of conditions due to its special structure with varying parameters. The robust D-stability of the multiple input and multiple output (MIMO) system is also addressed. It is shown that the D-stability performance of the L 2 point formation control system with parametric uncertainties can be ensured by using PEA controller. Finally, a simulation of formation flying is performed to illustrate the effectiveness of the proposed control approach.

Description: This paper considers an optimal control problem for switched stochastic systems. The controlled parameter consists of the switching times, and the cost criterion has the form of the mixed integral and endpoint cost terms of performance functions defined on the system's state trajectory. An approach to finding the optimal switching times is proposed. First, we derive the derivative of the cost with respect to the switching time for one switching time case. Then, for the problem with multi-switching times, we present the corresponding gradient formula. The obtained formulas have an especially simple form and can be directly used in gradient descent algorithms to locate the optimal switching instants. Finally, the validity of the proposed method is demonstrated by two numerical examples.

Description: The tension between the meaning of causality in science and law or public policy is well-known; however, defendants in product liability cases or industries that might be affected by a government regulation may try to convince the factfinder to require evidence of a causal relationship that meets the standards of science. From the perspective of public health, however, people may be exposed unnecessarily to a health risk during the time period between the establishment of reasonably strong evidence of a causal relationship and the overwhelming evidence required for scientific causality. The Bayesian paradigm enables one to update information from epidemiologic studies as they accumulate, providing estimates of the probability that the relative risk of a particular harm from exposure exceeds a threshold value, e.g. 2.0 or 4.0 that is sufficient to meet the preponderance of the evidence standard or to support a health initiative. In order to diminish the role of the initial prior distribution, which may be quite subjective, the first case-control study or an analysis of adverse event and case reports is used to determine two prior distributions. One is the most favourable to the defendant, or industry that might be regulated, which is consistent with the previous data. The other is centred on or near the estimated relative risk from the first study. The method is applied to the studies that linked aspirin use to Reye syndrome and demonstrates that the evidence of a causal association was sufficiently strong in 1982, when the Food and Drug Administration first proposed that the public be warned of the risk, to support the regulation. Thus, lives would have been saved had the warning been given at the end of 1982 rather than in early 1985.

Description: In law, inferences of causation are sometimes made through a structured process in which multiple participants play various roles, and make decisions concerning various logical components of the overall inference (such as legal rules, policy objectives, presumptions, evidence, burdens of proof and findings of fact). This article illustrates such a process using empirical research into compensation decisions in the USA for injuries allegedly caused by vaccinations. Empirical research into actual legal processes is essential, in order to discover how various players approach their sub-tasks of decision-making. It also provides insights for areas outside of law, such as non-monotonic logic, cognitive science, sociology and artificial intelligence.

Description: Situations of causal factual uncertainty are relatively common in law. The problems and difficulties regarding ‘factual causation’ in law point to the need of ‘evidence’ and ‘proof’ models that are adequate and capable to accommodate the tests and methodologies used to explain and demonstrate it in a legal context. Given the configuration of the situations of causal factual uncertainty and the available ‘evidence’ and ‘proof’ models, I argue that it is justified to use an ‘argumentative-narrative’ model for ‘proving causation’ in law. However, considering that each model of ‘evidence’ and ‘proof’ reveals a different kind of ‘rationality’ that can still be viewed in different ways, I also argue that we must try to match the perspective we have on the ‘rationality’ behind the chosen model of ‘evidence’ and ‘proof’ with the ‘rationality’ underlying ‘causation’ in law.

Description: At least in some cases, the values confronted in legal decision-making appear to be incommensurable. Some legal theorists resist incommensurability because they fear that this presents an overwhelming obstacle to rational decision-making. By offering a close analysis of proportionality and, more particularly, measures of proportional value satisfaction, I show that this fear is unfounded. Comparative measures of proportional value satisfaction do not require the values to be commensurable. However, assuming incommensurability presents us with the problem of public significance in the proportional satisfaction of values. When two values are commensurable, this public significance is provided by the mediating effects of the overarching third value that provides the common measure of the values. However, when this common measure is removed, then the public significance of value satisfaction must be otherwise achieved. This is why I propose an equal proportional value satisfaction as the most appropriate proportionality maximand. Under equal proportional value satisfaction, the proportional satisfaction of any one value has significance for each and every other value. This kind of public significance is interpersonal rather than impersonal (or second-personal rather than third-personal). The article then shows that the legal process that is most appropriate to equal proportionality is a process that implements defeasible legal rules.

Description: In order to allocate the risk between parties in legal adjudication, we use evidentiary techniques with the main device among them being the standard of proof (SoP). The traditional view holds the grade of probability to be the parameter that shifts when moving to different standards. However, as soon as we dig slightly deeper, an incoherent picture is being revealed. In this article, I challenge the accepted view and try to show that it faces insurmountable problems concerning the rationality, the grammatical consistency and the impact of the SoP for the acceptability of verdicts. At the end of the article, I shortly discuss the theory of epistemological contextualism and propose a framework that allows rational distinctions to be drawn between different standards of proof. In the second part of this project (forthcoming), I will defend a contextualist view according to which shifting parameter is not the grade of (aleatory) probability, but instead the Set of Epistemic Defeaters in play.

Description: This paper deals with the boundary control problems for the system described by first-order hyperbolic partial integro-differential equations with nonlocal boundary conditions by means of the deformation formulas. It is shown that the associated operator with nonlocal terms generates a C 0 -semigroup and the system defines an abstract boundary control system in L 2 -space. On the basis of the construction of integral kernel function, the ordinal and evolutional deformation formulas are established for a general class of Volterra integro-differential equations with nonlocal terms. By applying a special form of the formulas, a design of feedback boundary control law is given, which makes the scalar boundary control system null controllable in finite time. Furthermore, the null controllability result is extended to coupled nonsymmetric first-order hyperbolic systems by using appropriate linear transformations. Applications to physically important coupled systems are also given.

Description: This article focuses on the question of how decision makers with no relevant scientific background can (if at all) legitimately evaluate conflicting scientific expert testimonies and determine their relative reliability. Sceptics argue that non-experts can never reach justifiable conclusions regarding the merits of conflicting expert testimonies because they lack the fundamental epistemic capacity to make such judgement calls. In this article, I draw on works on epistemology, philosophy of practical reasoning, philosophy of science, science and technology studies, and legal theory in order to scrutinize recent proposals to solve the problem of conflicting scientific expert testimonies. Addressing this question is of ultimate importance due to the idea that immanent in the idea of rule-of-law there is an intellectual due process norm, which articulates that epistemically arbitrary legal decisions are also not legally justified. This article is divided into two Sections. In Section 2 , I describe the basic philosophical inquiries underlying the debate about expert testimony. In particular, I first elaborate on the philosophy of testimony and its epistemic justifications, then move to the idea of epistemic deference, and finish with philosophical accounts of expertise. Section 3 presents the problem of conflicting scientific expert testimonies and analyses recent attempts to solve it as formulated by Ward Jones, Alvin Goldman and Scott Brewer. I argue that there is no single criterion (or set of criteria) upon which the non-expert could rely in order to make a rationally justified decision in each and every case in which he faces conflicting scientific expert testimonies. The alternative view here defended is to stop looking for an epistemic panacea and accept the idea that testimonial reliability operates differently within different kinds of testimony—and differently within the same kind of testimony at different times.

Description: Adaptive sliding-mode strategies of first and second sliding orders are developed for single-input single-output systems of the first and second relative degrees, respectively. Since the only concrete known uncertainty bounds are assumed to be the upper bounds of logarithmic derivatives, no standard sliding-mode technique can solve the problem.

Description: This paper investigates the robust guaranteed cost control problem of uncertain stochastic hybrid complex delayed networks with Markovian jump parameters and external stochastic disturbances. The main goal of this paper is to design state-feedback controllers such that the complex networks achieve mean-square stability, and meanwhile the optimal upper bound of cost function is guaranteed. Based on Lyapunov–Krasovskii stability theory and Dynkin's formula, a sufficient condition for the existence of the optimal guaranteed cost control law is given in terms of linear matrix inequalities. A numerical example is given to illustrate the effectiveness of the proposed method.

Description: This paper investigates the forced second-order consensus problem in directed networks with time delays. First, a general forced consensus protocol is studied and some sufficient and necessary conditions on control parameters are obtained to guarantee the forced consensus; based on these conditions, several convenient methods for choosing parameters are provided. Then, by analysing the poles of the closed-loop system, the delay sensitivity of the protocol is investigated. The maximal upper bound of the allowable delays is provided. Simulation examples are presented to illustrate the effectiveness of the theoretical results.

Description: Let A + be the ring of Laplace transforms of complex Borel measures on R with support in [0,+) which do not have a singular nonatomic part. We compare the -metric d A + for stabilizable plants over A + given in Ball & Sasane (2012, Complex Analysis and Operator Theory , 6 , 65–89). with yet another metric d H | A + , namely the one induced by the metric d H for the set of stabilizable plants over H given in Sasane (2012, Mathematical Control and Related Fields , 2 , 29–44). Both d A + and d H coincide with the classical Vinnicombe metric defined for rational transfer functions, but we show here by means of an example that these two possible extensions of the classical -metric for plants over A + do not coincide on the set of stabilizable plants over A + . We also prove that they nevertheless give rise to the same topology on stabilizable plants over A + .

Description: The problems of delay-dependent robust stability and stabilization for discrete singular time-delay systems with norm-bounded uncertainties are investigated in this paper. By introducing some non-positive items to compensate the redundant energy caused by the positive items, an improved Lyapunov functional, namely partial non-positive (PNP) Lyapunov functional, is presented for achieving less conservative results. On the basis of the forward difference of this PNP Lyapunov functional, modified strict linear matrix inequality (LMI)-based delay-dependent conditions are established for the singular time-delay system to be regular, causal and stable. By solving these LMIs, an explicit expression for the desired state-feedback control law is obtained. Finally, numerical examples are given to illustrate that the proposed results are effective and less conservative than the existing ones.

Description: The criterion of bioequivalence of two drugs in infringement cases may differ from the requirements used for drug approval by the FDA. In Adams v . Perrigo , 1 the Federal Circuit examined three different sets of criteria for judging bioequivalence. The statistical properties of those criteria are explored and evaluated. Our results support the appellate court’s decision to impose less stringent requirements for bioequivalence in infringement cases.

Description: The North Carolina Racial Justice Act allows defendants to submit statistical studies of prosecutorial actions pertaining to their seeking the death penalty or in making peremptory challenges. These studies may consider data from four geographical regions: the state, county, judicial division or prosecutorial district. A study of the effect of race on peremptory challenges in death penalty cases demonstrating statistically significant disparities disadvantaging Black defendants has been submitted in several cases. This comment shows that a more appropriate statistical analysis yields much stronger statistical evidence that race entered into the peremptory challenge process in Randolph County than the affidavit submitted by the authors of the study. A subsequent sensitivity analysis indicates that in order for a characteristic to explain the highly statistically significant disparity, it would need to increase the odds of an individual being challenged by a factor of three and more than twice as many Black venire members would need to possess that characteristic as non-Blacks. Since the data examined excluded potential jurors who had been removed for cause, it may be difficult for the state to find a legitimate reason justifying the racial disparity.

Description: This article critically evaluates experiments used to justify inferences of specific source attribution (‘individualization’) to ‘100% certainty’ and ‘near-zero’ rates of error claimed by firearm toolmark examiners in court testimonies, and suggests approaches for establishing statistical foundations for firearm toolmarks practice that two recent National Academy of Science reports confirm do not currently exist. Issues that should be considered in the earliest stages of statistical foundational development for firearm toolmarks are discussed.

Description: Much debate exists between Frequentist and Bayesian methods in statistics. In the evaluation of evidence, the likelihood ratio is credited with quantifying the value of evidence in favour of one or other proposition by considering the probability of the evidence conditional on each proposition and this then converts the Bayesian prior odds into the posterior odds. Motivated by this approach, this paper considers an alternative p -value-based likelihood ratio by explicitly taking into account the behaviour of the Frequentist p -value under both hypotheses, rather than restricting focus solely on the null hypothesis. It is shown that by accommodating the alternative hypothesis, analysis leads to inferential conclusions which are consistent with Bayesian methods.

Description: This essay explores the implications of complexity for understanding both the law of evidence and the nature of the legal system. Among the propositions critically analysed is that one significant way to understand the general problem of the meaning of rationality is as a multivariate search for tools to understand and regulate a hostile environment. The law of evidence is conceptualized as a subset of this effort, at least in part, as involving a search for tools to regulate the almost infinitely complex domain of potentially relevant evidence and at the same time to accommodate policy demands. The proposition is then considered that the legal system of which the evidentiary system is a part has emergent properties that may not be deducible from its component parts, which suggests in turn that it may be, or at least has properties highly analogous to, a complex adaptive system. One implication of this analysis is that the tools of standard academic research that rely heavily on the isolation and reduction of analytical problems to manageable units to permit them to be subjected to standard deductive methodologies may need to be supplemented with analytical tools that facilitate the regulation of complex natural phenomena such as fluid dynamics. This has direct implications for such things as the conception of law as rules, and thus for the Hart–Dworkin debate that has dominated jurisprudence for 50 years. That debate may have mischaracterized the object of its inquiry, and thus the Dworkinian solution to the difficulties of positivism is inapplicable. It can certainly be shown that the Dworkinian solution is not achievable and cannot rationally be approximated. Solutions to legal problems within the legal system as a whole (as compared to any particular node within the legal system) are arrived at through a process of inference to the best explanation that occurs within a highly interconnected set of nodes similar to a neural or social network.

Description: Causation as an element of a criminal offence is different from the probative difficulties. The empirical laws that are relevant to the proof of causation, as a pure matter of fact, are not discussed here, but only causality as a category of our understanding and a general law of the intelligible world. This general law of causality is equally valid for all result crimes (e.g. homicide, bodily harm, deception offences and criminal damage). According to the European continental theory of conditions, any ‘conditio sine qua non’ is by itself a cause. Causation is established by the formula of ‘conditio’ (similar to the so-called ‘but for’ test in the common law), which corresponds to a counterfactual reasoning. However, that formula is not able to resolve adequately those cases of causal overdetermination where the result occurred by means of actions of multiple, independently intervening agents. A semantic model of the world evolution, based upon ramified temporal logic, may assist the comprehension of causal connections between human actions and the relevant results. At the end of the day, this model allows us to understand that even in situations where no kind of factual uncertainty is present, doubts upon the attribution of causation to specific agents remain. We shall conclude that the attribution of causation is not a natural problem, but a logico-legal one, that has to be dealt with by way of logico-legal criteria. Nevertheless, attribution of causation must be clearly distinguished from objective imputation of proscribed harm.

Description: In this paper, we investigate the problem of estimating the states of networked systems that involves random measurement and subject to nonstationary packet dropouts. The developed estimation algorithm is suitable for networked systems with any type of delays. Using the delay information in the measurement model, new and less conservative estimation conditions for networked systems are derived. The criterion is formulated in terms of linear matrix inequalities. An illustrative example is presented to show the applicability of the proposed design technique.

Description: This paper is concerned with the issue of passivity analysis for switched generalized neural networks (SGNNs). Parametric uncertainty is considered and assumed to be time-variant and norm bounded. We first give the passivity condition for SGNNs without uncertainties, and then extend the result to the cases with time-varying parametric uncertainties both in network parameters and output matrices. By using the Lyapunov–Krasovskii functional and some analysis techniques, the passivity criteria are presented in terms of linear matrix inequalities. Two numerical examples are given to show the effectiveness of the theoretical results.

Description: This paper addresses a problem of robust stabilization for a class of switched systems in the presence of bounded perturbations. We consider non-linear dynamic models under arbitrary switching mechanisms. The practical stabilization method we propose is carried out by a linear-type feedback switching control strategy subject to an average dwell-time scheme. We apply the newly elaborated (extended) version of the conventional invariant ellipsoid method for this purpose. The numerically implementable sufficient conditions for the practical stability of systems are derived using bilinear matrix inequalities. The obtained results are illustrated by the example of a continuous stirred tank reactor.

Description: So far, none (except the authors) in the literature proposes closed-form solutions of the number of reachable states for even the marked graphs, the simplest subclass of Petri nets, not to mention infinite systems (i.e. very large number of resources and process steps). This paper is the first one to tackle such issues by estimating reachable (forbidden, live and deadlock) states with a non-recursion and closed-form formula (depending on parameter k ) for a subclass of nets with k resources. As a result, we can deal with even an infinite system with infinite resources which nobody can ever do it. Extension to more than two processes has been briefly presented. Application to large Gadara RAS (resource allocation system) is also mentioned.

Description: In this paper, some new non-linear integral inequalities are established. These inequalities can be used in the study of stability problems of perturbed dynamic systems. As applications, based on these new inequalities, some sufficient conditions for global uniform asymptotic stability are obtained. A numerical example is presented to illustrate the applicability of the main result.

Description: In this paper, the controllability result of impulsive neutral stochastic functional differential equations with finite delay and fractional Brownian motion in a Hilbert space is studied. By using Banach's fixed point theorem, sufficient conditions are given for the controllability of the system. Finally, an example is given to illustrate the application of our result.

Description: The Bezier curves are presented to solve the optimal control problem with pantographs delays. Direct algorithm for solving this problem is given. We have chosen the Bezier curves as piecewise polynomials of degree n , and determine Bezier curves on [ t 0 , t f ] by n +1 control points. Numerical examples illustrate that the algorithm is applicable, and very easy to use.

Description: This paper considers time-delay systems with bounded disturbances. We study a new problem of finding an upper bound of an absolute value function of any given linear functional of the state vector starting from the origin of the system. Based on the Lyapunov–Krasovskii method combining with the recent Wirtinger-based integral inequality that has just been proposed by Seuret & Gouaisbaut (2013. Wirtinger-based integral inequality: application to time-delay systems. Automatica , 49 , 2860–2866), sufficient conditions for the existence of an upper bound of the function are derived. The obtained results are shown to be more effective than those adapted from the existing works on reachable set bounding. Furthermore, the obtained results are applied to refine existing ellipsoidal bounds of the reachable sets. The effectiveness of the obtained results is illustrated by two numerical examples.

Description: This paper is concerned with the problem of the exponential state estimation for switched neural networks with uncertain parameters. Based on the theories of the switched systems and available output measurements, the mathematical model of the switched interval estimation error system under the switching rule with average dwell time is established. Multiple Lyapunov–Krasovskii functions are employed to ensure the stability of the switched estimation error system for all admissible time delays; both the existence conditions and the explicit characterization of the desired estimator are derived in terms of linear matrix inequalities. Moreover, the sufficient conditions for guaranteeing the robust exponential stability of switched interval neural networks with discrete and distributed time delays are easily derived. Finally, two numerical examples are provided to illustrate the validity of the theoretical results.

Description: This paper generalizes previous optimal upper bounds on the minimum Euclidean distance for phase shift keying (PSK) block codes, that are explicit in three parameters: alphabet size, block length and code size. The bounds are primarily generalized from codes over symmetric PSK to codes over asymmetric PSK and also to general alphabet size. Furthermore, block codes are optimized in the presence of other types of noise than Gaussian, which induces also non-Euclidean distance measures. In some instances, codes over asymmetric PSK prove to give higher Euclidean distance than any code over symmetric PSK with the same parameters. We also provide certain classes of codes that are optimal among codes over symmetric PSK.

Description: This paper addresses the stabilization problem for a class of genetic regulatory networks (GRNs) with mixed delays which include both the finite distributed time delay and the discrete time delay. The adaptive feedback control scheme is adopted to achieve the global asymptotic stability for the GRNs. By resorting to the integral partitioning technique and the delay fractioning approach, a novel Lyapunov–Krasovskii functional is constructed, and some sufficient criteria are established to ensure the closed-loop GRNs to be globally asymptotically stable. The conditions obtained are in the form of matrix inequalities and easy to be solved by resorting to the standard softwares in the Matlab. Finally, a numerical example is given to demonstrate the applicability and efficiency of the proposed approach.

Description: The definition of weighted entropy allows to calculate the entropy of the mixture of measures. In this paper, we investigate the problem of equivalent definition of the general entropy function in the weighted form. We show that under a reasonable condition, which is satisfied by the well-known Shannon, Rényi and Tsallis entropies, every entropy function can be defined equivalently in the weighted way. As a corollary, we show how to use the weighted form to compute Tsallis entropy of the mixture of measures.

Description: In the literature are given several equivalent conditions for the strict positive realness property of transfer function matrices. Recently, it is shown that some of these equivalent conditions are not fully matched with the definition of strict positive realness. On the other hand, there is a necessary condition in the recent statements which is difficult to check and this difficulty is strongly increased when the number of system poles or the dimension of the transfer function matrix of the system is increased. In addition, there is not a correct statement for characterizing strictly positive real (SPR) improper transfer function matrices yet. In this paper, we remove these deficiencies and derive a more complete version of necessary and sufficient conditions for characterizing SPR multivariable systems. For this purpose, we use Taylor series expansion and Laurent series expansion simultaneously. To illustrate the ease and comprehensiveness of our results, we present several illustrative examples.

Description: In this paper, the switching signal and passive control of uncertain discrete switched systems with interval time-varying delay and linear fractional perturbations are investigated. Some of the LMI criteria are provided to design the switching signal and passive control of discrete switched time-delay system. Non-negative inequalities are introduced to reduce the conservativeness of the proposed results. Finally, a numerical example is illustrated to show the main proposed results.

Description: This paper considers the optimal estimation of linear systems over unreliable communication channels with random delays. In this work, it is assumed that the system to be estimated is far away from the filter. The observations of the system are capsulized without time stamp and then transmitted to the network node at which the filter is located. The probabilities of time delays are assumed to be known. The event-driven estimation scheme is applied in this paper and the estimate of the states is updated only at each time instant when any measurement arrives. To capture the feature of communication, the system considered is augmented, and the arrived measurements are regarded as the uncertain observations of the augmented system. The corresponding optimal estimation algorithm is proposed and additionally, a numerical simulation represents the performance of this work.

Description: In this paper, stabilization of a chain of fractional-order integrators is attempted. The stability is proved using contraction analysis. A numerical example is presented to illustrate the proposed method.

Description: This paper deals with the asymptotic hyperstability of switched time-varying dynamic systems involving switching actions among linear time-invariant parametrizations in the feed-forward loop for any feedback regulator controller potentially being also subject to switching through time while being within a class which satisfies a Popov-type integral inequality. Asymptotic hyperstability is proved to be achievable under very generic switching laws if at least one of the feed-forward parametrization possesses a strictly positive real transfer function, a minimum residence time interval is respected for each activation time interval of such a parametrization and a maximum allowable residence time interval is simultaneously maintained for all active parametrizations which are not positive real, if any. In the case where all the feed-forward parametrizations possess a common Lyapunov function, asymptotic hyperstability of the switched closed-loop system is achieved under arbitrary switching.

Description: This paper presents a dynamic linear output feedback controller for global stabilization of a class of non-linearly parametrized systems subject to time-delay. By introducing two adaptive strategies, we first construct a dynamic linear output feedback controller with two dynamic gains. After that, with the aid of an appropriate Lyapunov–Krasovskii functional, the adaptive strategies are explicitly given to dominate the time-delay non-linearities bounded by higher-order parametrized growth conditions and render the closed-loop system globally asymptotically stable. Some new results on output feedback stabilization of non-linear systems with time-delay and unmeasurable states are provided. The first result is proposed for the global stabilization of non-linearly parametrized systems with time-delay. And the second one studies the dynamic linear output feedback controller which is under more general higher-order growth conditions than the existing results. The correctness of the theoretical results are illustrated with several academic simulation examples.

Description: We investigate an everywhere defined notion of solution for control systems whose dynamics depend non-linearly on the control u and state x , and are affine in the time derivative . For this reason, the input u , which is allowed to be Lebesgue integrable, is called impulsive , while a second, bounded measurable control v is denominated ordinary. The proposed notion of solution is derived from a topological (non-metric) characterization of a former concept of solution which was given in the case when the drift is v -independent. Existence, uniqueness and representation of the solution are studied, and a close analysis of effects of (possibly infinitely many) discontinuities on a null set is performed as well.

Description: Recent maximally permissive deadlock prevention controls for systems of simple sequential processes with resources (S 3 PR) also aim at constructing simplest structures in the shortest amount of time for flexible manufacturing systems modelled by Petri nets. The paper in Liu et al. (2013, IMA J. Math. Control Inf. , doi:10.1093/imamci/dnt029) proposes a method to merge several monitors into a single one while not losing the live states. It achieves the same best results in the existing literature while avoiding the time-consuming reachability analysis which does not scale well with the large size of the nets. For a well-known benchmark, the method needs one more monitor than other approaches. Thus, siphon-based merging may not achieve minimal configuration. Although we could reduce one monitor, which monitor to choose to merge seem to be ad hoc . It is unclear how to select a monitor to reduce for large nets. This paper tackles such an issue successfully.

Description: Based on the integral sliding mode control method, some theoretical criteria for the robust synchronization of multi-coupled general non-linear systems with external disturbances are presented, the ultimate error bounds are estimated simultaneously. Furthermore, as an application, the detailed analysis and conclusions are derived for a network of multi-coupled FitzHugh–Nagumo (FHN) systems with external disturbances. Finally, some numerical examples, with two or more coupled FHN systems, are given to illustrate the effectiveness of the proposed theoretical results.

Description: This paper provides necessary conditions and sufficient conditions for the (global) input-to-state stability property of simple uncertain vehicular-traffic network models under the effect of a PI regulator. Local stability properties for vehicular-traffic networks under the effect of PI regulator control are studied as well: the region of attraction of a locally exponentially stable equilibrium point is estimated by means of Lyapunov functions. All obtained results are illustrated by means of simple examples.

Description: We discuss a class of linear control problems in a Hilbert space setting. This class encompasses such diverse systems as port-Hamiltonian systems, Maxwell's equations with boundary control or the acoustic equations with boundary control and boundary observation. The boundary control and observation acts on abstract boundary data spaces such that the only geometric constraint on the underlying domain stems from requiring a closed range constraint for the spatial operator part, a requirement which for the wave equation amounts to the validity of a Poincare–Wirtinger-type inequality. We also address the issue of conservativity of the control problems under consideration.

Description: This paper concerns with the problem of state bounding for a class of discrete-time Markovian jump systems with interval time-varying delay. By constructing a new Lyapunov–Krasovskii functional combining with the delay-decomposition technique and the reciprocally convex approach, new delay-range-dependent conditions are derived ensuring that all state trajectories of the system are mean square bounded. These conditions are derived in terms of matrix inequalities which can be computationally solved to find a smallest possible bound of mean square. A numerical example is provided to verify the effectiveness of the obtained result.

Description: Non-deterministic firing of concurrent transitions in Petri nets (PNs) may lead to the information loss of conflicts. The phenomenon is called confusions that usually occur in the evolution of a PN containing interlaced conflicting and concurrent transitions, which generates incomplete and faulty system conflicting behaviour such that conflicts cannot be correctly resolved. This paper investigates detection and avoidance approaches of confusions in safe PNs. First, the structural features of confusions are characterized and two detection algorithms are proposed to capture confusion subnets in a PN according to their structural features. Secondly, a method of supervisory control is developed to avoid the occurrence of confusions in a PN. It contains a policy of the generation of confusion avoidance constraints and a method to synthesize supervisors enforcing a class of place and enabling degree constraints, P/E constraints for short. Finally, an example of confusion detection and avoidance in an automated manufacturing system is presented.

Description: Limited frequency interval Gramians-based model reduction techniques for generalized non-singular systems are presented. These techniques generalize the results of existing limited frequency interval Gramians schemes for general non-singular systems. Numerical examples are also presented to illustrate the effectiveness of proposed techniques.

Description: A numerical method using Haar wavelets for solving fractional optimal control problems (FOCPs) is studied. The fractional derivative in these problems is in the Caputo sense. The operational matrix of fractional Riemann–Liouville integration and the direct collocation method are considered. The proposed technique is applied to transform the state and control variables into non-linear programming (NLP) parameters at collocation points. An NLP solver can then be used to solve FOCPs. Illustrative examples are included to demonstrate the validity and applicability of the proposed method.

Description: On the basis of Awad sup-entropy, the efficiency function for type I censored sample from the Pareto distribution and the relative loss of entropy due to censoring are derived. The properties of the derived efficiency are discussed. Furthermore, for a given efficiency, the termination time of the experiment, the maximum likelihood estimate and a confidence interval for the Pareto shape parameter are introduced when the location parameter is known.

Description: This paper addresses the dynamic output feedback control design problem for limited bandwidth and sampled-data dynamical systems, under the so-called local sensor – remote actuator setting. As a first approach, a suboptimal solution to the periodic sampled-data control problem is developed and it is shown that this solution presents the celebrated separation property . Based on this result, we provide two more general designs, which are well-adapted to practical applications in limited bandwidth networked environments. The first one is a robust controller, in which the data rate is a bounded, unknown and time-varying variable. The second one is a self-triggered controller, which improves the closed-loop performance by adequately choosing the sampling instants. Several examples validate the developed theory and point out its main potentialities.

Description: This paper is concerned with the feedback stabilization problem for a rotating rigid body-beam system via a torque control exerted on the rigid body and a time-dependent delayed dynamic boundary force control acting at the free end of the beam. Sufficient conditions on the angular velocity of the rigid body and the delay term are derived to assure the existence and uniqueness of solutions to the system. Furthermore, the energy method approach is employed to establish the exponential stability of the closed-loop system under stronger but reasonable assumptions.

Description: This paper considers the problem of designing the robust weighted fusion steady-state Kalman smoothers for multisensor system with uncertain noise variances. Applying the augmented state method, the problem of designing the robust Kalman smoothers can be converted into that of designing the equivalent robust Kalman filters. According to the minimax robust estimation principle and the unbiased linear minimum variance optimal estimation rule, based on the worst-case conservative system with conservative upper bounds of noise variances, the local and five weighted fusion robust steady-state Kalman smoothers are presented. For all admissible uncertainties of noise variances, the minimal upper bound of the actual smoothing error variances is given. A Lyapunov equation approach for the robustness analysis is presented, the concept of robust accuracy is presented, and the robust accuracy relations of the local and fused robust Kalman smoothers are proved. A simulation example verifies the robustness and robust accuracy relations.

Description: We prove the existence of mild solutions of fractional integro-differential equations with non-local conditions in Banach spaces. Sufficient conditions for controllability of fractional integro-differential systems are established. The results are obtained by using resolvent operators and Schauder fixed point theorem. An example is provided to illustrate our results.

Description: This paper establishes a new robust delay-dependent stabilization and $H_{\infty }$ control methods for a class of uncertain stochastic time-delay systems. The delays in state and control input are time-varying continuous functions varying in an interval and uncertainties are norm-bounded. An appropriate Lyapunov–Krasovskii functional is constructed and a new technique to estimate the upper bound of the stochastic differential of Lyapunov–Krasovskii functional is obtained. Based on the idea of delay decomposition and free-weighting matrices, new and less conservative solutions to the stabilization and $H_{\infty }$ control problem of uncertain stochastic time-delay systems are provided in terms of linear matrix inequalities. A robust state feedback controller is proposed to guarantee mean-square asymptotic stability as well as the prescribed $H_{\infty }$ performance for the closed-loop systems. The advantages of the results proposed in this paper, which differ greatly from most of the existing results, lie in their reduced conservatism by thinning the delay partitioning. Numerical examples are provided to show the advantages of the proposed technique.

Description: In this paper, a non-fragile controller is presented for multivariable bilinear systems via state feedback. The controller fragility can be described as the sensitivity of the controller to variations in controller parameters. The proposed method leads to the synthesis of controller which is non-fragile towards a special form of uncertainty in the controller parameters. Based on the Lyapunov method, the stability conditions of the overall closed loop multivariable bilinear systems in the presence of the additive controller gain variations are formulated in terms of solutions to a linear matrix inequality (LMI). Sufficient conditions for the existence of desired controller gains are given in terms of LMI. Important issues for the stability analysis and design are remarked. Finally, a numerical example and a practical application of a Headbox control system of paper-making machine are given to illustrate the design procedure and performance of our proposed controller with comparative results.

Description: In previous work, it has been shown that novel interval-based sliding mode techniques can be employed effectively for the design of guaranteed stabilizing control strategies for high-temperature fuel cells. These control strategies aim at both trajectory tracking during non-stationary heating phases and at compensating disturbances at desired constant operating points. The implementation of the corresponding control strategies involves three main building blocks: (i) transformation of the state equations into a non-linear controller canonical form, (ii) application of interval arithmetic techniques in real time for the computation of stabilizing system inputs despite bounded uncertainty and (iii) an online optimization for the synthesis of the input variables, namely suitable preheater mass flows and temperatures. For practical application, the transformation into the controller canonical form based on the computation of Lie derivatives can be impeded by the complexity of the symbolic representation of the state equations. Hence, techniques for algorithmic differentiation are compared in this contribution with alternative approaches based on symbolic formula manipulation. The latter one is only efficient for low-dimensional finite volume models in the description of thermodynamic system behaviour. Since the interval-based control law involves the use of time derivatives of the measured or estimated system output up to its relative degree, suitable differentiation techniques using low-pass filtered derivatives, algebraic derivative estimation and sensitivity-based approaches conclude this contribution in a numerical comparison.

Description: This brief is concerned with $H\infty$ filtering problem for singularly perturbed systems (SPSs) with variable sampling and probabilistic missing measurements. The signal received from sensor is sampled by a sampler with variable sampling periods before it is employed by the designed filter. By using an input delay approach, the $H\infty$ filtering problem is reduced to the $H\infty$ filter design for SPSs with bounded time delays. Moreover, the measure missing problem is considered, and the missing probability for each sensor is governed by an individual random variable satisfying a certain probabilistic distribution in the interval [0 1]. Sufficient conditions for the existence of the admissible filter are derived in terms of $\varepsilon$ -independent linear matrix inequalities, which ensure the asymptotic stability as well as a prescribed $H\infty$ performance for the filtering error dynamics. A simulation example is presented to demonstrate the effectiveness of proposed filtering scheme.

Description: In this paper, a novel three-dimensional autonomous chaotic system, the so-called Dadras–Momeni system, is considered and two different control techniques are employed to realize chaos control and chaos synchronization. First, the optimal control of the chaotic system is discussed and an open loop feedback controller is proposed to stabilize the system states to one of the system equilibria, minimizing the cost function by virtue of the Pontryagin's minimum principle. Then, an adaptive control law and an update rule for uncertain parameters, based on Lyapunov stability theory, are designed both to drive the system trajectories to an equilibrium or to realize a complete synchronization of the system in periodic and chaotic regimes. Numerical simulations are included to show the effectiveness of the designed controllers in realizing the stabilization and the synchronization of the chaotic system. Finally, a new hyperchaotic system is introduced by adding a controller to the second equation of the three-dimensional autonomous Dadras–Momeni chaotic system and the corresponding hyperchaotic attractor is shown via computer simulations.

Description: This paper presents the methods used to simultaneously estimate states and unknown information for a class of non-linear systems, and the unknown information consists of both input uncertainty and output disturbance. The state and output transformations are adopted to decouple the input uncertainty, and a reduced-order system of the original system is constructed. By taking the output disturbance vector as an extended state vector, the constructed reduced-order system is transformed into an augmented singular system. For the singular system, based on LMI techniques the states and output disturbance are simultaneously estimated by designing a singular system observer. Then a high-gain sliding mode observer is considered to obtain the exact estimation of output derivatives in a finite time, and a kind of algebraic input uncertainty estimation method is proposed by using the estimates of the states and output derivatives. Finally, a simulation example is given to illustrate the effectiveness of the proposed methods.

Description: This paper considers the robustness issue on switching time of switched systems, in which each switching point has perturbation for a small variation. Our goal is to find optimal switching instants such that the system's performance being resistant against perturbations. By using the integral averaging technique and combining with optimal control theory, the derivatives of the cost function with respect to the original switching times are derived. We focus on the fixed switching mode sequences and use a gradient-descent algorithm to find the optimal switching instants. The efficacy of the proposed method is illustrated via numerical examples.

Description: This work considers the computation of rigorous componentwise time-varying bounds on the states of a non-linear control system. This work develops a new implementation of an existing bounding theory that exploits physical information to produce tight bounds. It is shown that the solution of a certain initial value problem in ordinary differential equations (ODEs) depending on parametric linear programs (LPs) (which are said to be ‘embedded’) yields componentwise bounds. To ensure the numerical tractability of such a formulation, some properties of the resulting system of ODEs with LPs embedded are discussed. Finally, the tightness of the bounds are demonstrated for models of reacting chemical systems with uncertain rate parameters.

Description: In this paper, switched non-linear systems in parametric strict feedback form with uncertainty, disturbance and unknown time delay are considered. At first, by using adaptive backstepping approach a common Lyapunov function (CLF) is found and a robust adaptive control is designed to stabilize the system against disturbance and unknown time delays. In continuance a modified adaptive backstepping approach is introduced, which makes it easier to find a CLF. At the end, simulation results are provided to show the effectiveness of the proposed approaches.

Description: In this paper, we explore an approach to check the exponential stability of the distributed parameter system with non-collocated feedback. We regard the characteristic determinant as an entire function with parameters that usually are the feedback gains. By checking that there is no zero of this entire function on the imaginary axis for some parameters, we assert that there is no spectrum of the system in the closed right half-plane. Further, we check the Riesz basis property of the eigenvectors of the system, and hence get the exponential stability of the system. As an example, we study a hybrid system consisting of one-dimensional wave equation with tip mass and non-collocated feedback. By finding out the condition of no spectrum on the imaginary axis, we determine the exponential stability region of the parameters of the hybrid system.

Description: This work develops models and numerical methods for controlled regime-switching systems that stem from a mean-variance formulation. Distinct from the prior treatments, the switching process is a hidden Markov chain. Assuming a noisy observation of switching process corrupted by white noise is available, we focus on minimizing the variance subject to a fixed terminal expectation. Using the Wonham filter, we convert the partially observable system to a completely observable one first. Because closed-form solutions are virtually impossible to obtain, our main effort is devoted to designing a numerical algorithm. Convergence of the algorithm is obtained. A numerical example is provided to demonstrate the results.

Description: This paper is concerned with the problem of robust H filter design for a class of Markovian jump neural networks (MJNNs) with random sensor failure, mode-dependent time-varying delays and norm-bounded parameter uncertainties. We aim to design mode-dependent and random sensor failure filter which ensures that the filtering error system is not only exponentially mean-square stable, but also satisfies a prescribed H -norm level for all admissible uncertainties, and extend this result to a class of stochastic MJNNs. A stochastic Lyapunov–Krasovskii function is proposed to reflect the mode-dependent time-varying delays, and a set of strict linear matrix inequalities are utilized to derive sufficient conditions that guarantee the desired filter can be constructed. Two numerical examples are presented to illustrate the effectiveness and usefulness of the main results obtained.

Description: In this work, a class of game-theoretic Riccati differential equations with periodic coefficients occurring in connection with stochastic H control problem is considered. An iterative algorithm for the computation of the stabilizing solution of this kind of Riccati differential equations with indefinite sign is proposed.

Description: The methodology of stability analysis of the twisting and super-twisting control systems is based on similarity of their equations with those for passive second-order mechanical systems. The approach makes designing Lyapunov functions transparent: they are the sum of kinetic and potential energies. Finite time convergence at the presence of disturbances is demonstrated along with estimations of the convergence time and upper level of admissible disturbances.

Description: An analogue chaotic system is not stable under the influence of noise and environment, thus it is not suitable for some practical use, such as cryptographic application. Therefore, a more efficient way is to use digital systems. Trying to realize the chaotic systems in digital computers with computing precisions always leads a dynamical degradation of chaotic properties. Some methods for improving the dynamical degradation of digital chaotic systems have been proposed; however, none of them has solved this problem, except for improving some of the chaotic properties. In this paper, we propose an analogue–digital mixed method for solving the dynamical degradation of digital chaotic system. We prove that the analogue–digital mixed system is chaotic under Wiggins's chaos definition. Some numerical experiments are also given in this paper.

Description: A new adaptive control design method based on dynamic scaling and filter for high-order lower triangular system is given, which does not satisfy the certainty equivalence principle. The proposed practically adaptive state feedback controller that ensures all signals of closed-loop systems are globally bounded while keeping the output tracking error to an arbitrary small neighbourhood of the origin simultaneously. The proposed method relies on a novel parameter estimator proposed in Karagiannis & Astolfi (2008, Syst. Control Lett. , 57 , 733–739). Finally, a numerical example is given.

Description: The current practice of Malaysian courts in calculating the award of damages for loss of future earnings in personal injury and fatal accidents claims is the conventional multiplier–multiplicand approach without admitting any actuarial evidence. The objective is to calculate an appropriate amount to compensate the plaintiff which will restore to the position he would have been in if that particular damage had not occurred. This article attempts to develop actuarial models using the concept of human life value that can be used as a guide to determine the amount of loss of future earnings. We believe this is where actuarial scientists need to play a role in developing a new scientific model in order to acquire an appropriate amount of award, which is relevant and satisfy both plaintiff and defendant.

Description: Recently published articles have proposed the use of likelihood ratios (LRs) in determining the evidential value of finding a given number of gunshot residue (GSR) particles on a suspect. LRs depend on the probabilistic models assumed for the defence proposition (the suspect was not involved in a shooting) and the prosecutor’s proposition (the suspect was involved), and should be calculated based on data obtained in well designed experiments. However, statistical aspects of the analysis that select the appropriate model and provide uncertainty measures are rarely considered. In this article, data from Cardinetti et al. (2006 , A proposal for statistical evaluation of the detection of gunshot residues on a suspect. Scanning , 28 (3):142–147) are used to demonstrate the sensitivity of calculated LRs to the assumed model. It is shown that the Poisson model, considered by Cardinetti and others, is inappropriate and that a Negative Binomial model fits the data much better. The statistical error arising from the fact that models are estimated based on small sampled data is discussed, as well as the importance of accounting for this error. We conclude that only with a large database can statistical models be estimated accurately and LR’s be treated as valid scientific measures.

Description: We first discuss certain problems with the classical probabilistic approach for assessing forensic evidence, in particular its inability to distinguish between lack of belief and disbelief, and its inability to model complete ignorance within a given population. We then discuss Shafer belief functions, a generalization of probability distributions, which can deal with both these objections. We use a calculus of belief functions which does not use the much criticized Dempster rule of combination, but only the very natural Dempster–Shafer conditioning. We then apply this calculus to some classical forensic problems like the various island problems and the problem of parental identification. If we impose no prior knowledge apart from assuming that the culprit or parent belongs to a given population (something which is possible in our setting), then our answers differ from the classical ones when uniform or other priors are imposed. We can actually retrieve the classical answers by imposing the relevant priors, so our set-up can and should be interpreted as a generalization of the classical methodology, allowing more flexibility. We show how our calculus can be used to develop an analogue of Bayes’ rule, with belief functions instead of classical probabilities. We also discuss consequences of our theory for legal practice.

Description: A non-linear adaptive observer is proposed to estimate the unmeasured states of a class of time-delay non-linear systems. Irrespective of the size of the constant delay, it is shown that the observer is globally convergent if the growth rate of the system non-linearities is output dependent. The presented results generalize previous results on observation of Lipschitz time-delay systems. Subsequently, the observer-based control problem of time-delay systems, having triangular structure, is discussed for arbitrary large constant delay.

Description: In this paper, applying the Rothe's Fixed Point Theorem, we prove the approximate controllability of the following semilinear Beam equation: \[\left \{\begin {align}\frac {\partial ^{2} y(t,x) }{\partial t^{2}} U)\ (U=L^{2}(\Omega ))$ and the non-linear function $f:[0,\tau ]\times {\mathbb {R}}\times {\mathbb {R}}\times {\mathbb {R}}\longrightarrow {\mathbb {R}}$ is smooth enough and there are $\eta , b, c\in {\mathbb {R}}$ with $\frac {1}{2}\leq \eta \leq 1$ such that \[|f(t,y,v,u)|\lt b|u|^{\eta } +c\quad \forall y,v,u\in {\mathbb {R}},\] We prove that for all $\tau 〉 0$ this system is approximately controllable on $[0,\tau ]$ .

Description: We examine linear programming (LP) based relaxations for synthesizing polynomial Lyapunov functions to prove the stability of polynomial ordinary differential equations (ODEs). Our approach starts from a desired parametric polynomial form of the polynomial Lyapunov function. Subsequently, we encode the positive definiteness of the function, and the negation of its derivative, over the domain of interest. We first compare two classes of relaxations for encoding polynomial positivity: relaxations by sum-of-squares (SOS) programmes, against relaxations based on Handelman representations and Bernstein polynomials, that produce linear programmes. Next, we present a series of increasingly powerful LP relaxations based on expressing the given polynomial in its Bernstein form, as a linear combination of Bernstein polynomials. Subsequently, we show how these LP relaxations can be used to search for Lyapunov functions for polynomial ODEs by formulating LP instances. We compare our techniques with approaches based on SOS on a suite of automatically synthesized benchmarks.

Description: This paper is mainly concerned with the approximate controllability of fractional stochastic integro-differential equations with infinite delay of order $1\lt \alpha \lt 2$ . Sufficient conditions for approximate controllability of fractional control system are proved under a range condition on the control operator and the corresponding linear fractional control system is approximately controllable. The results are obtained by using the stochastic analysis techniques and fixed point theory. Further, we extend the result to study the approximate controllability of fractional stochastic differential equations driven by Poisson jumps. An example is given to illustrate the theory.

Description: In this paper, the non-fragile observer-based passive control problem is discussed for a class of systems with repeated scalar non-linearities and time-varying delays. The non-linear system is defined by a discrete-time state equation containing a repeated scalar non-linearity. The system under consideration is modelled by assuming the random imperfect communication links existing between the controller and observer. The random fluctuations are defined by utilizing the Bernoulli distributed white sequences. The non-fragile observer-based feedback controller gains are designed to guarantee that the considered closed-loop control system with repeated scalar non-linearities and time-varying delays is passive. Sufficient conditions are derived for the existence of controller and observer gains by using the Lyapunov stability theory, passivity theory and linear matrix inequalities. As a final point, a numerical example by using a marketing-production system is presented to demonstrate the effectiveness of the proposed theoretical results.

Description: This paper deals with the problem of robust stochastic exponential stability for uncertain stochastic systems with multiple delays. Based on the extended reciprocally convex approach, some novel delay-dependent stability criteria with less conservatism and less decision variables for the addressed system are derived. At last, some numerical examples are presented to show the effectiveness and improvement of the proposed results.

Description: This paper is concerned with the optimal distributed control problem of the Kuramoto–Sivashinsky equation with pointwise state constraints and coupled integral state-control constraints. Based on perturbation methods of modern variational analysis and Ekeland's variational principle, the Pontryagin's minimum principle of this system is proved. The main difficulty in this paper is to deal with the non-linear term in the Kuramoto–Sivashinsky equation.

Description: In this paper, the asymptotic stability of uncertain discrete switched systems with interval time-varying delay and linear fractional perturbations is achieved via switching signal design. Some linear matrix inequality (LMI) stability criteria are provided to design the switching signal by the proposed non-uniform delay-partitioning approach. Finally, some numerical examples are illustrated to show the main developed results.

Description: A definition of causality introduced by Halpern & Pearl, which uses structural equations , is reviewed. A more refined definition is then considered, which takes into account issues of normality and typicality, which are well known to affect causal ascriptions. Causality is typically an all-or-nothing notion: either A is a cause of B or it is not. An extension of the definition of causality to capture notions of degree of responsibility and degree of blame , due to Chockler and Halpern, is reviewed. For example, if someone wins an election 11–0, then each person who votes for him is less responsible for the victory than if he had won 6–5. Degree of blame takes into account an agent's epistemic state. Roughly speaking, the degree of blame of A for B is the expected degree of responsibility of A for B , taken over the epistemic state of an agent. Finally, the structural-equations definition of causality is compared to Wright’s NESS test.

Description: The European Court of Justice has held that as from 21 December 2012, insurers may no longer charge men and women differently on the basis of scientific evidence that is statistically linked to their sex, effectively prohibiting the use of sex as a factor in the calculation of premiums and benefits for the purposes of insurance and related financial services throughout the European Union. This ruling marks a sharp turn away from the traditional view that insurers should be allowed to apply just about any risk assessment criterion, so long as it is sustained by the findings of actuarial science. The naïveté behind the assumption that insurers’ recourse to statistical data and probabilistic analysis, given their scientific nature, would suffice to keep them out of harm’s way was exposed. In this article, I look at the flaws of this assumption and question whether this judicial decision, whilst constituting a most welcome landmark in the pursuit of equality between men and women, has nonetheless gone too far by saying too little on the million dollar question of what separates admissible criteria of differentiation from inadmissible forms of discrimination.

Description: A study by the authors of determining manner of death used a method novel to forensic pathology. This article details the method used. Drawing on the methodology of evidence-based medicine, data was systematically identified and pooled to provide a robust and substantial dataset of probabilities for forensic evidential features of gunshot wounds. This provided source data for a Bayesian analysis to determine the probable manner of death. We suggest the same method can be applied to a wide variety of evidence, meeting the need for strong and reliable data highlighted by R v . T and subsequent debate.

Description: The Engineering Department of the Spanish Civil Guard has been using automatic speaker recognition systems for forensic purposes providing likelihood ratios since 2004. They are quantitatively much more modest than in the DNA field. In this context, it is essential a suitable calculation of the prior odds to figure out the posterior odds once the comparison result is expressed as likelihood ratio. These odds are under the responsibility of a Judge, and many consider unlikely that they can be quantitatively calculated in real cases. However, our experience defending in Court over 500 speaker recognition expert reports allows us to suggest how the expert may support Judges from a technical point of view to assess the odds. Technical support as referred should be preferentially provided in the preliminary investigation stage, after the expert report being issued by the laboratory, as in the course of oral hearings it is much more difficult for those who are not familiar with the new paradigm. It can be initiated upon request by the Examining Judge or any of the litigant parties. We consider this practice favourable to the equality of arms principle. The use of Bayesian networks is proposed to provide inferential assistance to the Judge when assessing the prior odds. An example of the explanation above is provided by the case of the terrorist attack against Madrid-Barajas Airport Terminal 4 perpetrated in December 2006.

Description: The role played by the required level of statistical significance in the scientific method should not be seen as analogous to that played by the standard of proof in the legal process.

Description: The Supreme Court ruled in Matrixx that statistical significance is not necessary to show that a drug caused an adverse reaction. Five circuit court decisions holding otherwise preceded this decision. This paper examines the extent to which the Supreme Court’s reasoning differed from those of the circuit courts.

Description: Unlike the evaluation of single items of scientific evidence, the formal study and analysis of the joint evaluation of several distinct items of forensic evidence has to date received some punctual, rather than systematic, attention. Questions about the (i) relationships among a set of (usually unobservable) propositions and a set of (observable) items of scientific evidence, (ii) the joint probative value of a collection of distinct items of evidence as well as (iii) the contribution of each individual item within a given group of pieces of evidence still represent fundamental areas of research. To some degree, this is remarkable since both, forensic science theory and practice, yet many daily inference tasks, require the consideration of multiple items if not masses of evidence. A recurrent and particular complication that arises in such settings is that the application of probability theory, i.e. the reference method for reasoning under uncertainty, becomes increasingly demanding. The present paper takes this as a starting point and discusses graphical probability models, i.e. Bayesian networks, as framework within which the joint evaluation of scientific evidence can be approached in some viable way. Based on a review of existing main contributions in this area, the article here aims at presenting instances of real case studies from the author’s institution in order to point out the usefulness and capacities of Bayesian networks for the probabilistic assessment of the probative value of multiple and interrelated items of evidence. A main emphasis is placed on underlying general patterns of inference, their representation as well as their graphical probabilistic analysis. Attention is also drawn to inferential interactions, such as redundancy, synergy and directional change. These distinguish the joint evaluation of evidence from assessments of isolated items of evidence. Together, these topics present aspects of interest to both, domain experts and recipients of expert information, because they have bearing on how multiple items of evidence are meaningfully and appropriately set into context.

Description: In its first foray into the labyrinth that causation in personal injury has become, the U.K. Supreme Court recently held obiter that statistical evidence alone could not establish causation. But in an earlier toxic tort case, the High Court had relied on epidemiological evidence to identify a cluster of birth defects arising in the vicinity of a contaminated land site. This recent British experience is then discussed within the wider context of the forensic role of ‘naked statistics’.