ALBERT

Description: 〈p〉Publication date: Available online 10 July 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of the Franklin Institute〈/p〉 〈p〉Author(s): Yaonan Shan, Kun She, Shouming Zhong, Jun Cheng, Wenyong Wang, Can Zhao〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉This paper investigates the passivity of Markovian jump discrete-time systems (MJDTSs) with channel fading via event-triggered state feedback control. First, the concerned MJDTSs contain infinitely distributed delays and switching rules with partially known transition probability (TP) information. Next, the fading channel, as an unreliable channel, is introduced into MJDTSs to better reflect the engineering practice in networked environment. Due to the present of channel fading, a series of random variables satisfying some certain probability density functions (PDFs) will be obstacles in the process of proof. Then, an event-triggered controller is designed for MJDTSs with channel fading and incomplete transition probability (ITP) for the first time. Thanks to this event-triggered mechanism, the state feedback control could greatly reduce energy consumption during transmission. Subsequently, under the above controller, we obtain some novel sufficient criteria in the form of linear matrix inequalities (LMIs) to ensure the passivity of closed-loop system. Finally, some simulation results are provided to demonstrate the feasibility and effectiveness of the proposed theoretical method.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 10 July 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of the Franklin Institute〈/p〉 〈p〉Author(s): Ahmed Bendib, Aissa Chouder, Kamel Kara, Abdelhammid Kherbachi, Said Barkat, Walid Issa〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉In a microgrid (MG) topology, the secondary control is introduced to compensate for the voltage amplitude and frequency deviations, mainly caused by the inherent characteristics of the droop control strategy. This paper proposes an accurate approach to derive small signal models of the frequency and amplitude voltage at the point of common coupling (PCC) of a single-phase MG by analyzing the dynamics of the second-order generalized integrator-based frequency-locked loop (SOGI-FLL). The frequency estimate model is then introduced in the frequency restoration control loop, while the derived model of the amplitude estimate is introduced for the voltage restoration loop. Based on the obtained models, the MG stability analysis and proposed controllers’ parameters tuning are carried out. Also, this study includes the modeling and design of the synchronization control loop that enables a seamless transition from island mode to grid-connected mode operation. Simulation and practical experiments of a hierarchical control scheme, including traditional droop control and the proposed secondary control for two single-phase parallel inverters, are implemented to confirm the effectiveness and the robustness of the proposal under different operating conditions. The obtained results validate the proposed modeling approach to provide the expected transient response and disturbance rejection in the MG.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 4 July 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of the Franklin Institute〈/p〉 〈p〉Author(s): Xi Wang, Shukai Li, Tao Tang〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉With the objective to promote the efficiency of heavy haul transportation, this paper investigates the efficiently intermittent cruise control problem for heavy haul trains. Based on the concept of periodically intermittent control, the closed-loop form of the error dynamic state-space model for heavy haul trains is given considering uncertain parameters, which is different from existing heavy haul train control methods in that the control forces are only provided in part of the running period. To facilitate the controller design, a set of linear matrix inequalities (LMIs) are presented as the sufficient conditions for the existence of the periodically intermittent controller, which guarantees both the speed tracking error and the relative coupler displacements are exponentially stable at the equilibrium state. Simulation results indicate that the proposed control scheme can significantly improve the control efficiency without sacrificing too much on speed tracking performance.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 4 July 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of the Franklin Institute〈/p〉 〈p〉Author(s): Xin Hu, Chi Huang, Jianquan Lu, Jinde Cao〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉This paper studies the stabilization problem of Boolean control networks with stochastic impulses, where stochastic impulses model is described as a series of possible regulatory models with corresponding probabilities. The stochastic impulses model makes the research more realistic. The global stabilization problem is trying to drive all states to reach the predefined target with probability 1. A necessary and sufficient condition is presented to judge whether a given system is globally stabilizable. Meanwhile, an algorithm is proposed to stabilize the given system by designing a state feedback controller and different impulses strategies. As an extension, these results are applied to analyze the global stabilization to a fixed state of probability Boolean control networks with stochastic impulses. Finally, two examples are given to demonstrate the effectiveness of the obtained results.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 29 August 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of the Franklin Institute〈/p〉 〈p〉Author(s): Quanxin Zhu, S. Vimal Kumar, R. Raja, Fathalla Rihan〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉This paper addresses the issue of reliable feedback control of an uncertain aircraft flight control systems with disturbances via non-fragile sampled-data control approach. In particular, the parameter uncertainties are assumed to be randomly occurring which is described by the Bernoulli distributed sequences. By constructing a suitable Lyapunov-Krasovskii functional together with Wirtinger-based inequality, a new set of sufficient conditions in terms of linear matrix inequalities is obtained to ensure the asymptotic stability and extended dissipativity of the aircraft flight control systems not only when all actuators are operational, but also in case of some actuator failures. Finally, simulation results are conducted to validate the effectiveness of the proposed control design technique.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 21 August 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of the Franklin Institute〈/p〉 〈p〉Author(s): Cheng Tan, Zhongchang Liu, Wing Shing Wong〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉This paper investigates the formation control of interconnected second-order systems. Each agent is assumed to be capable of measuring its own absolute velocity and the relative positions with respect to its neighboring agents, whereas the target formation is described by absolute positions of all agents in a global coordinate. For such formation control problems, no distributed control policy was reported in existing literature. This paper focuses on the string connection structure of the agents and proposes a distributed control policy that takes the form of purely state feedback without incorporating any feed-forward component. The closed-loop system equation is characterized by an oscillation matrix whose entries are the feedback controller gains. Formation control is accomplished by formulating the agents’ target positions as feedback controller gains. Moreover, it is shown that for agent models described by double integrators, each of the agents located at the two endpoints of the string structure should know its own absolute position. For a class of agent models where each agent’s acceleration depends on its own position, the control laws do not need to use the absolute position. For both system models, the target formations that are asymptotically reachable by the proposed control laws are specified explicitly. Numerical simulations have been conducted to illustrate the effectiveness of the theoretical results.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 31 July 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of the Franklin Institute〈/p〉 〈p〉Author(s): Zhengjiang Zhang, Junghui Chen〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉The design, tuning, and implementation of controllers are crucial for the solutions to control problems. Generalized minimum variance control (GMVC) has attractive properties and it is widely used for controller performance enhancement. The measured signals of process output variables, which are used as feedback signals, are generally subject to measurement noise. However, the GMVC theory assumes the feedback signals are the process outputs, which rarely consider the unavoidable measurement noise. By additionally considering the measurement noise, the control performance of GMVC with the measurement noise is analyzed in this paper. The dynamic data reconciliation (DDR) method, which uses the information of both the process model and the measurement data to reconcile the measured signals, is introduced. It is combined with GMVC to reduce the effect of the measurement noise on the results of GMVC. The effectiveness of GMVC combined with DDR is illustrated in two case studies, where the proposed method is compared with the original GMVC and the GMVC with the conventional digital filter. The results in both SISO and MIMO control systems show that the proposed GMVC combined with DDR can reduce the effect of the measurement noise and achieve better control performance.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 31 July 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of the Franklin Institute〈/p〉 〈p〉Author(s): P. Baziana, G. Fragkouli, E. Sykas〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉In this paper we study a multi-channel network, each station of which is equipped with a network interface that has a receiver buffer of multiple packets. In this way, each station is able to receive multiple packets per time instant. We adopt a synchronous access protocol which is affected by the collisions over the multiple channels and the destination conflicts. The proposed protocol performance crucially depends on the size of the receiver buffer since it determines the packet rejection probability at destination. An analytical probabilistic model based on a Markovian process is adopted for the performance measures derivation by means of closed mathematical formulas. The proposed protocol is compared to relative ones that either totally ignore the receiver collisions or assume a receiver buffer of a single packet capacity. The numerical results show that the increase of the receiver buffer size improves the performance decisively, resulting in higher throughput and lower delay and rejection probability. Also, it is shown that the appropriate receiver buffer size per station in order for the rejections at destination to be effectively eliminated is not unlimited but is limited to three packets for 0.1% accepted maximum level of rejection probability.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 17 August 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of the Franklin Institute〈/p〉 〈p〉Author(s): Chengyang Luo, Jianyong Yao, Jason Gu〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉This paper presents an extended state observer-based output feedback adaptive controller with a continuous LuGre friction compensation for a hydraulic servo control system. A continuous approximation of the LuGre friction model is employed, which preserves the main physical characteristics of the original model without increasing the complexity of the system stability analysis. By this way, continuous friction compensation is used to eliminate the majority of nonlinear dynamics in hydraulic servo system. Besides, with the development of a new parameter adaption law, the problems of parametric uncertainties are overcome so that more accurate friction compensation is realized. For another, the developed adaption law is driven by tracking errors and observation errors simultaneously. Thus, the burden of extended state observer to solve the remaining uncertainties is alleviated greatly and high gain feedback is avoided, which means better tracking performance and robustness are achieved. The designed controller handles not only matched uncertainties but also unmatched dynamics with requiring little system information, more importantly, it is based on output feedback method, in other words, the synthesized controller only relies on input signal and position output signal of the system, which greatly reduces the effects caused by signal pollution, measurement noise and other unexpected dynamics. Lyapunov-based analysis has proved this strategy presents a prescribed tracking transient performance and final tracking accuracy while obtaining asymptotic tracking performance in the presence of parametric uncertainties only. Finally, comparative experiments are conducted on a hydraulic servo platform to verify the high tracking performance of the proposed control strategy.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 9 August 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of the Franklin Institute〈/p〉 〈p〉Author(s): Engin H. Copur, Ahmet C. Arican, Sinan Ozcan, Metin U. Salamci〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉State Dependent Riccati Equation (SDRE) methods have the considerable advantages over other nonlinear control methods. However, stability issues can be arisen in SDRE based control system due to the lack of the global asymptotic stability property. Therefore, the previous studies have usually shown that local asymptotic stability can be ensured by estimating a Region of Attraction (ROA) around the equilibrium point. These estimated regions for stability may become narrow or the condition to keep the states in this region may be very conservative. To resolve these issues, this paper proposes a novel SDRE method employing an update algorithm to re-estimate the ROA when the states tend to move out of the stable region. The tendency is checked using a condition which is developed based on a new theorem. The theorem proves that it is possible to redesign the previous ROA with respect to the current states lying close to its boundary for ensuring the “non-local” stability along the trajectory without the need of solving SDRE at each time instant, unlike the standard SDRE approach. Therefore, the new theorem is now able to enhance the stability of the SDRE based closed-loop control system. The feasibility of the proposed SDRE control method is tested in both simulations and experiments. A validated 3-DOF laboratory helicopter is used for experiments and the control objective for the helicopter is to realise a preplanned movement in both elevation and travel axes. The results reveal that the proposed SDRE approach enables the controlled plant to track the desired trajectory as satisfactorily as the standard SDRE approach, while only solving SDRE when needed. The proposed SDRE method reduces the computational load for practical implementation of the control algorithm whilst ensuring the stability over the operational region.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 1 August 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of the Franklin Institute〈/p〉 〈p〉Author(s): Yi Dong, Shengyuan Xu〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉This paper studies the rendezvous problem for a class of linear systems with uncertain parameters and external disturbances under the state-dependent dynamic network, which is also called rendezvous network here. By combining potential function technique, distributed internal model design and adaptive control technique, a distributed adaptive state feedback control law is proposed to solve the rendezvous problem by completing the tasks of maintaining the connectivity of the rendezvous network, achieving asymptotic tracking, rejecting unknown external disturbances as well as handling uncertain parameters in the system dynamics, the leader system and the exosystem simultaneously.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 31 July 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of the Franklin Institute〈/p〉 〈p〉Author(s): R. Kavikumar, R. Sakthivel, O.M. Kwon, B. Kaviarasan〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉This paper is concerned with the issue of finite-time boundedness of discrete-time uncertain interval type-2 fuzzy systems with time-varying delay and external disturbances via an observer-based reliable control strategy. According to the system output variable, a full-state observer that shares the same membership functions of the plant is constructed to estimate the unknown system states. In addition, a reliable controller subject to observer states and actuator faults is designed to formulate the closed-loop feedback control system, which does not share the same membership functions of the plant. Then, by constructing an appropriate Lyapunov–Krasovskii functional and using the finite-time stability theory, a new set of delay-dependent sufficient conditions guaranteeing the finite-time boundedness of the addressed system is established in the framework of linear matrix inequalities. Furthermore, the explicit expressions of gain matrices of the state observer and the reliable controller are given in terms of the established sufficient conditions. Finally, simulation results are presented to demonstrate the effectiveness of the obtained theoretical results.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 17 August 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of the Franklin Institute〈/p〉 〈p〉Author(s): Kaixian Ba, Bin Yu, Qixin Zhu, Zhengjie Gao, Guoliang Ma, Zhengguo Jin, Xiangdong Kong〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉In this paper, the hydraulic drive unit(HDU) driving the joint motion of the legged robot is the research object. Through the experiment on HDU, it is observed that the control accuracy of the traditional position-based impedance control is not high enough. The further analysis researches the serial-parallel composition on dynamic compliances from both position control inner and impedance outer loop. Then, the two reasons affecting control accuracy are found out. Therefore, aimed at the first reason, a compliance-eliminated controller with multiple serial branches is designed. Aimed at the second reason, a feedforward compensation controller is designed. Finally, the dynamic compliance composition is rearranged. The results of experiments conducted indicate that the proposed method significantly improves the control accuracy compared to that of traditional position-based impedance control.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 9 August 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of the Franklin Institute〈/p〉 〈p〉Author(s): Zhihuan Chen, Xiaohui Yuan, Xiaotao Wu, Yanbin Yuan, Xiaohui Lei〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉This paper investigates the frequency change problem of hydraulic turbine regulating system based on terminal sliding mode control method. By introducing a novel terminal sliding mode surface, a global fast terminal sliding mode controller is designed for the closed loop. This controller eliminates the slow convergence problem which arises in the terminal sliding mode control when the error signal is not near the equilibrium. Meanwhile, following consideration of the error caused by the actuator dead zone, an adaptive RBF estimator based on sliding mode surface is proposed. Through the dead zone error estimation for feed-forward compensation, the composite terminal sliding mode controller has been verified to possess an excellent performance without sacrificing disturbance rejection robustness and stability. Simulations have been carried out to validate the superiority of our proposed methods in comparison with other two other kinds of sliding mode control methods and the commonly used PID and FOPID controller. It is shown that the simulation results are in good agreement with the theoretical analysis.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 7 August 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of the Franklin Institute〈/p〉 〈p〉Author(s): Youmei Zhou, Jianwei Xia, Hao Shen, Jianping Zhou, Zhen Wang〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉The paper addresses the issue of extended dissipative learning for a class of delayed recurrent neural networks. Both time-varying delay and time-invariant delay are taken into account. By choosing appropriate Lyapunov–Krasovkii functionals and utilizing some inequalities, several weight learning rules are developed for ensuring the network to be asymptotically stable and extended dissipative. The existence conditions for these learning strategies consist of a few linear matrix inequalities, which are able to be verified readily by Matlab software. Two numerical examples are employed to show the effectiveness and low conservatism of the proposed learning rules.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 6 August 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of the Franklin Institute〈/p〉 〈p〉Author(s): Ticao Jiao, Ju H. Park, Cunshan Zhang, Yanlei Zhao, Kefeng Xin〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉This paper deals with the stability problem of a class of stochastic switching singular systems with jumps, where all the continuous subsystems can be unstable. By introducing multiple time-varying discretized Lyapunov functions and designing novel switching signals via mode-dependent dwell times, sufficient conditions ensuring mean square and almost sure stabilities of the considered systems are obtained. On the basis of these findings, some existing results in the literature are further generalized. We finally provide a numerical example to verify the applicability of the proposed theoretical results.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 5 August 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of the Franklin Institute〈/p〉 〈p〉Author(s): Xinhe Wang, Zhen Wang, Jianwei Xia〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉In this paper, a delayed fractional eco-epidemiological model with incommensurate orders is proposed, and a control strategy of this model is discussed. Firstly, for the system with no controller, the stability and Hopf bifurcation with respect to time delay are investigated. Secondly, under the influence of the controller, the stability and Hopf bifurcation of the system is discussed, and it is indicated that the stability of the system can be changed by increasing the feedback control delay. In particular, a separate study is carried out on the bifurcation with respect to the extended feedback delay, and the bifurcation point is calculated. At last, to support the theoretical results, some numerical simulations are depicted.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 16 August 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of the Franklin Institute〈/p〉 〈p〉Author(s): Junyuan Yang, Chairat Modnak, Jin Wang〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉Cholera is an infectious disease caused by the bacterium vibrio cholerae, which can lead to widespread epidemics in the deterioration of public health systems or the associated infrastructure. Vaccination and water sanitation are two well-known methods for the prevention and intervention of cholera epidemics. In this paper, we propose an age-structured cholera model that incorporates both the environment-to-human and human-to-human transmission pathways and that includes host vaccination and water sanitation as disease control measures. We rigorously investigate the threshold dynamics of this model using the basic reproduction number derived from our analysis. Meanwhile, we perform an optimal control study to explore cost-effective intervention strategies for cholera. Our numerical simulation results show that the outcome of the optimal control is shaped by the complex interactions among the age structure of the hosts, the costs of the control measures, the transmission modes of the disease, and the different approaches of cholera intervention.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 16 August 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of the Franklin Institute〈/p〉 〈p〉Author(s): Xing Fang, Fei Liu〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉A novel coupling and disturbance characterization based control (CDC-BC) scheme is investigated for manned submersibles with strong couplings and disturbances. Firstly, the coupling characterization index (CCI) and disturbance characterization index (DCI) are defined to indicate whether the couplings and disturbances harm or benefit the manned submersible system. Then, the coupling and disturbance characterization based control (CDC-BC) method is developed to eliminate the detrimental couplings and disturbances, as well as to retain the beneficial ones. Moreover, it is also proved that the tracking errors of the closed-loop system will converge to zero asymptotically. Finally, some simulation results demonstrate the effectiveness of the proposed control scheme.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 7 August 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of the Franklin Institute〈/p〉 〈p〉Author(s): S.H. Lee, M.J. Park, O.M. Kwon, R. Sakthivel〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉In this work, a sampled-data control problem for neural-network-based systems with an optimal guaranteed cost is investigated. By constructing suitable time-dependent functionals and utilizing an improved free-matrix-based integral inequality, a sampled-data stability criterion for neural-network-based systems is derived. Based on a first result, a sampled-data controller design method for neural-network-based systems that meets the maximum sampling period and minimum guaranteed cost performance is proposed. The superiority and validity of the results will be verified by comparing with the existing results in a numerical example.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 1 November 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of the Franklin Institute〈/p〉 〈p〉Author(s): Yang Wang, Jing Yao, Guanrong Chen〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉An evolving super-network model with inter-vehicle communications (IVC) is established in this paper, which consists of two layers: the traffic network and the communication network. The model incorporates key parameters of wireless communication devices (characterized by their transmission ranges and bandwidths), market penetration rate and vehicle distribution. The impacts of these parameters on the topological structure of the model are revealed and verified via simulations using a modified car-following model with inter-vehicle communications. Finally, some guidelines are presented for adapting the topological organization of the communication network to the environment by tuning the key parameters.〈/p〉〈/div〉

Description: 〈p〉Publication date: January 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of the Franklin Institute, Volume 356, Issue 1〈/p〉 〈p〉Author(s): Gang Wang, Mohammed Chadli, Haihong Chen, Zhijin Zhou〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉This paper presents a novel event-triggered 〈em〉H〈/em〉〈sub〉∞〈/sub〉 static output-feedback control for active vehicle suspension systems with network-induced delays. The proposed control schema introduces an event-triggering mechanism in the suspension system such that the communication resources can be significantly saved. By applying some improved slack inequalities and an augmented Lyapunov–Krasovskii functional (LKF), a new design condition expressed in the form of linear matrix inequalities (LMIs) is developed to derive the desired event-triggered controller. The obtained algorithm is then employed to solve the static output-feedback control gain. Compared with the traditional sampled-data 〈em〉H〈/em〉〈sub〉∞〈/sub〉 control scheme, the proposed controller is able to provide an enhanced disturbance attenuation level while saving the control cost. Finally, comparative simulation results are provided to show the performance of the proposed event-triggered controller.〈/p〉〈/div〉

Description: 〈p〉Publication date: October 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of the Franklin Institute, Volume 355, Issue 15〈/p〉 〈p〉Author(s): Lin Zhang, Gang Li〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉The paper is concerned with the stability and stabilization problems for a family of hybrid linear parameter-varying systems with stochastic mode switching. The switching phenomenon is modeled by a semi-Markov stochastic process which is more generalized than a Markov stochastic process. With the construction of a Lyapunov function that depends on both the parameter variation and operating mode, numerical testable stability and stabilization criteria are established in the sense of 〈em〉σ〈/em〉-error mean square stability with the aid of some mathematical techniques that can eliminate the terms containing products of matrices. To test the effectiveness of the designed stabilizing controller, we apply the developed theoretical results to a numerical example.〈/p〉〈/div〉

Description: 〈p〉Publication date: January 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of the Franklin Institute, Volume 356, Issue 1〈/p〉 〈p〉Author(s): Yang Li, Hongbin Zhang〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉In this paper, the stability, 〈em〉L〈/em〉〈sub〉1〈/sub〉-gain analysis and asynchronous 〈em〉L〈/em〉〈sub〉1〈/sub〉-gain control problems of uncertain discrete-time switched positive linear systems (DSPLSs) with dwell time are investigated. First, several convex and non-convex conditions on dwell time stability of DSPLSs with interval and polytopic uncertainties are presented, and the relation between these conditions is revealed. Then, via a switched dwell-time-dependent co-positive Lyapunov functions (SDTLFs) approach, convex sufficient conditions on 〈em〉L〈/em〉〈sub〉1〈/sub〉-gain analysis and asynchronous 〈em〉L〈/em〉〈sub〉1〈/sub〉-gain control of DSPLSs with interval uncertainties are derived. Meanwhile, via the switched parameter-dwell-time-dependent co-positive Lyapunov functions (SPDTLFs) approach, the 〈em〉L〈/em〉〈sub〉1〈/sub〉-gain analysis and asynchronous 〈em〉L〈/em〉〈sub〉1〈/sub〉-gain controller design problems of DSPLSs with polytopic uncertainties are also solved. The stability and 〈em〉L〈/em〉〈sub〉1〈/sub〉-gain analysis results are given in terms of linear programming (LP). The controller design results are presented in terms of bilinear programming (BP), which can be solved with the help of iterative algorithm. At last, both numerical and practical examples are provided to show the effectiveness of the results.〈/p〉〈/div〉

Description: 〈p〉Publication date: November 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of the Franklin Institute, Volume 355, Issue 17〈/p〉 〈p〉Author(s): Shihua Fu, Jianli Zhao, Jianjun Wang〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉We investigate the input–output decoupling problem of switched Boolean control networks (SBCNs) in this paper. Based on the matrix expression of Boolean functions, the dynamics of SBCNs are converted into an algebraic form via semi-tensor product of matrices first. Then, using the redundant variable separation technique, we give the necessary and sufficient conditions for the existence of three kinds of controllers to detect whether an SBCN can be input–output decomposed or not, respectively, including the open-loop controllers, the state feedback controllers, and the output feedback controllers. Meanwhile, a constructive procedure is presented to construct the open-loop controllers, as well as the state feedback controllers and output feedback controllers. Finally, an illustrative example is given to show that the new results obtained are effective.〈/p〉〈/div〉

Description: 〈p〉Publication date: November 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of the Franklin Institute, Volume 355, Issue 16〈/p〉 〈p〉Author(s): Takanobu Imae, Kai Cai〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉In this paper, we study the algebraic connectivity of directed complex networks with scale-free property. Algebraic connectivity of a directed graph is the eigenvalue of its Laplacian matrix whose real part is the second smallest. This is known as an important measure for the diffusion speed of many diffusion processes over networks (e.g. consensus, information spreading, epidemics). We propose an algorithm, extending that of Barabasi and Albert, to generate directed scale-free networks, and show by simulations the relations between algebraic connectivity and network size, exponents of in/out-degree distributions, and minimum in/out degrees. The results are moreover compared to directed small-world networks, and demonstrated on a specific diffusion process, reaching consensus.〈/p〉〈/div〉

Description: 〈p〉Publication date: November 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of the Franklin Institute, Volume 355, Issue 17〈/p〉 〈p〉Author(s): Junyan Yu, Li He〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉We study scaled group consensus problems of the first/second-order multi-agent dynamics under continuous/discrete-time settings. For a directed multi-agent network with finite sub-networks, the scaled group consensus is concerned with this case that all the sub-networks reach consensus, separately, while maintain the given ratios among the multiple consensus. First/second-order distributed protocols with continuous/discrete data are designed to solve the scaled group consensus problems, and then necessary and sufficient criteria are established to guarantee the agents’ states reaching the scaled group consensus asymptotically applying both algebraic and analytical tools. Finally, the effectiveness of the theoretical results are verified by several simulation examples.〈/p〉〈/div〉

Description: 〈p〉Publication date: October 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of the Franklin Institute, Volume 355, Issue 15〈/p〉 〈p〉Author(s): Wenjie Si〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉This paper proposes an adaptive observer-based neural controller for a class of uncertain large-scale stochastic nonlinear systems with actuator delay and time-delay nonlinear interactions, where drift and diffusion terms contain all state variables of their own subsystem. First, a state observer is established for estimating the unmeasured states, and a predictor-like term is utilized to transform the input delayed system into the delay-free system. Second, novel appropriate Lyapunov–Krasovskii functionals are used to compensate the time-delay terms, and neural networks are employed to approximate unknown nonlinear functions. At last, an output-feedback adaptive neural control scheme is constructed by using Lyapunov stability theory and backstepping technique. It is shown that the designed neural controller can ensure that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded (SGUUB) and the tracking error is driven to a small neighborhood of the origin. The simulation results are presented to further show the effectiveness of the proposed approach.〈/p〉〈/div〉

Description: 〈p〉Publication date: October 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of the Franklin Institute, Volume 355, Issue 15〈/p〉 〈p〉Author(s): Guodong Wang, Xiangyu Wang, Shihua Li〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉In this paper, both leaderless and leader-follower consensus problems for a class of disturbed second-order multi-agent systems are studied. Based on integral sliding-mode control, sliding-mode consensus protocols are proposed for leaderless and leader-follower multi-agent systems with disturbances, respectively. Firstly, for leaderless second-order multi-agent systems, a sliding-mode consensus protocol is proposed to make the agents achieve asymptotic consensus. Secondly, for leader-follower second-order multi-agent systems, a finite-time sliding-mode consensus protocol is designed to make the agents achieve consensus in finite time. Both kinds of consensus protocols inherit the anti-disturbance performance and robustness of sliding-mode control and require less communication information. Finally, two numerical simulations are given for leaderless and leader-follower second-order multi-agent systems to validate the efficiency of the proposed consensus protocols.〈/p〉〈/div〉

Description: 〈p〉Publication date: October 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of the Franklin Institute, Volume 355, Issue 15〈/p〉 〈p〉Author(s): Xin Liu, Xianqiang Yang, Weili Xiong〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉Robust identification of the linear parameter varying (LPV) finite impulse response (FIR) model with time-varying time delays is considered in this paper. A robust observation model based on Laplace distribution is established to deal with the output data contaminated with the outliers, which are commonly existed in modern industries. A Markov chain model is utilized to model the correlation between the time delays as they do not simply change randomly in reality. A transition probability matrix and an initial probability distribution vector are used to govern the switching mechanism of the time delays. Since it is difficult to optimize the complex log likelihood function directly, the derivations of the proposed algorithm are performed under the framework of Expectation-Maximization (EM) algorithm. A numerical example and a chemical process are utilized to verify the effectiveness of the proposed approach.〈/p〉〈/div〉

Description: 〈p〉Publication date: October 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of the Franklin Institute, Volume 355, Issue 15〈/p〉 〈p〉Author(s): Chun Zeng, Dong Shen, JinRong Wang〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉This paper considers the adaptive iterative learning control (ILC) for continuous-time parametric nonlinear systems with partial structure information under iteration-varying trial length environments. In particular, two types of partial structure information are taken into account. The first type is that the parametric system uncertainty can be separated as a combination of time-invariant and time-varying part. The second type is that the parametric system uncertainty mainly contains time-invariant part, whereas the designed algorithm is expected to deal with certain unknown time-varying uncertainties. A mixing-type adaptive learning scheme and a hybrid-type differential-difference learning scheme are proposed for the two types of partial structure information cases, respectively. The convergence analysis under iteration-varying trial length environments is strictly derived based on a novel composite energy function. Illustrative simulations are provided to verify the effectiveness of the proposed schemes.〈/p〉〈/div〉

Description: 〈p〉Publication date: October 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of the Franklin Institute, Volume 355, Issue 15〈/p〉 〈p〉Author(s): Tiedong Ma, Tiantian Yu, Bing Cui〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉This paper mainly focuses on the adaptive synchronization problem of multi-agent systems via distributed impulsive control method. Different from the existing investigations of impulsive synchronization with fixed time impulsive inputs, the proposed distributed variable impulsive protocol allows that the impulsive inputs are chosen within a time period (namely impulsive time window) which can be described by the distances of the left (right) endpoints or the centers between two adjacent impulsive time windows. Obviously, this kind of flexible control scheme is more effective in practical systems (especially for the complex environment with physical restrictions). Moreover, the proposed adaptive control technique is helpful to solve the problem with uncertain system parameters. By means of Lyapunov stability theory, impulsive differential equations and adaptive control technique, three sufficient impulsive consensus conditions are given to realize the synchronization of a class of multi-agent nonlinear systems. Finally, two numerical simulations are provided to illustrate the validity of the theoretical analysis.〈/p〉〈/div〉

Description: 〈p〉Publication date: November 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of the Franklin Institute, Volume 355, Issue 16〈/p〉 〈p〉Author(s): Hai Liu, Maiying Zhong, Yang Liu〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉For the purpose of fault detection and isolation (FDI), reconstruction-based contribution (RBC) analysis is carried out in a model-based way. A bank of adaptive observers are designed for a set of potential faults. From these observers, fault estimates and fault signatures are directly available, thus contribution functions are conveniently constructed to accomplish the FDI work. This integrated design of contribution analysis and adaptive observer takes advantages of both data-driven and model-based approaches, and the diagnosis performance is improved. Furthermore, quantitative isolability analysis is also studied by similarity measurement of the obtained fault signatures. Simulation study with a nonlinear unmanned aerial vehicle (UAV) model shows the effectiveness of the proposed method.〈/p〉〈/div〉

Description: 〈p〉Publication date: November 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of the Franklin Institute, Volume 355, Issue 16〈/p〉 〈p〉Author(s): R. Bardhan, D. Ghose〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉This paper addresses a finite-time rendezvous problem for a group of unmanned aerial vehicles (UAVs), in the absence of a leader or a reference trajectory. When the UAVs do not cooperate, they are assumed to use Nash equilibrium strategies (NES). However, when the UAVs can communicate among themselves, they can implement cooperative game theoretic strategies for mutual benefit. In a convex linear quadratic differential game (LQDG), a Pareto-optimal solution (POS) is obtained when the UAVs jointly minimize a team cost functional, which is constructed through a convex combination of individual cost functionals. This paper proposes an algorithm to determine the convex combination of weights corresponding to the Pareto-optimal Nash Bargaining Solution (NBS), which offers each UAV a lower cost than that incurred from the NES. Conditions on the cost functions that make the proposed algorithm converge to the NBS are presented. A UAV, programmed to choose its strategies at a given time based upon cost-to-go estimates for the rest of the game duration, may switch to NES finding it to be more beneficial than continuing with a cooperative strategy it previously agreed upon with the other UAVs. For such scenarios, a renegotiation method, that makes use of the proposed algorithm to obtain the NBS corresponding to the state of the game at an intermediate time, is proposed. This renegotiation method helps to establish cooperation between UAVs and prevents non-cooperative behaviour. In this context, the conditions of time consistency of a cooperative solution have been derived in connection to LQDG. The efficacy of the guidance law derived from the proposed algorithm is illustrated through simulations.〈/p〉〈/div〉

Description: 〈p〉Publication date: October 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of the Franklin Institute, Volume 355, Issue 15〈/p〉 〈p〉Author(s): Bei Wang, Zhichao Li, Xuefeng Yan〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉In modern plant-wide systems, chemical industry processes are usually equipped with multiple operating modes to meet the requirements of diversification products. Accurately identifying the running-on mode therefore becomes a focal point. Meanwhile, systems produce numerous process variables, along with complex relationships, which may deteriorate the effectiveness with which statistical processes are monitored. To solve this problem, this study proposes a multimode factor analysis (FA) method that integrates Pearson's correlation coefficient, joint probability, and support vector data description (SVDD). First, subspaces are generated automatically by using Pearson's coefficients of correlation among variables, instead of based on prior knowledge, which is not always available. Second, the statistical indices are derived by the FA models constructed in each subspace and each mode. Third, the running-on mode is identified according to the joint probabilities among the statistical indices. Finally, SVDD is adopted to provide an intuitive indication for fault detection. The efficiency and availability of the proposed method are demonstrated by three case studies: a numerical simulation, the continuous stirred-tank reactor (CSTR) model, and the Tennessee Eastman (TE) benchmark process.〈/p〉〈/div〉

Description: 〈p〉Publication date: November 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of the Franklin Institute, Volume 355, Issue 17〈/p〉 〈p〉Author(s): Min-Rong Chen, Guo-Qiang Zeng, Xiao-Qing Xie〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉How to design a set of optimal distributed load frequency controllers for a multi-area interconnected power system is an important but still challenging issue in the field of modern electric power systems. This paper presents an adaptive population extremal optimization-based extended distributed model predictive load frequency control method called PEO-EDMPC for a multi-area interconnected power system. The key idea behind the proposed method is formulating the dynamic load frequency control issue of each area power system as an extended distributed discrete-time state-space model based on an extended state vector, obtaining a distributed dynamic extended predictive model, and rolling optimization of real-time control output signal by adopting an adaptive population extremal optimization algorithm, where the fitness is evaluated by the weighted sum of square predicted errors and square future control values. The superiority of the proposed PEO-EDMPC method to a traditional distributed model predictive control method, a population extremal optimization-based distributed proportional-integral control algorithm and a traditional distributed integral control method is demonstrated by the simulation studies on two-area and three-area interconnected power systems in cases of normal, perturbed system parameters and dynamical load disturbances.〈/p〉〈/div〉

Description: 〈p〉Publication date: Available online 25 September 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of the Franklin Institute〈/p〉 〈p〉Author(s): Yi Yang, Sixin Wang, Meilin Wen, Wei Xu〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉In this paper, a new evaluation method of reliability and security in cyber-physical system (CPS) considering communication failures is proposed based on instantaneous availability (IA) model and its fluctuation analysis. In this new method, IA model of CPS is established using the 〈em〉Markov〈/em〉 process principle, and three types of system states, namely, working state, repairing state and delay-repairing state, are discussed from the perspective of reliability and security. On the basis of the locking error, the numerical solution of the model is solved by the fourth order 〈em〉Runge〈/em〉–〈em〉Kutta〈/em〉 method, and the instantaneous availability of the CPS is proved to be fluctuating. Finally, the impact of different parameters on the instantaneous availability of fluctuations and the ways to suppress fluctuations and improve the CPS reliability are obtained by analyzing the instantaneous availability of different parameters.〈/p〉〈/div〉

Description: 〈p〉Publication date: November 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of the Franklin Institute, Volume 355, Issue 16〈/p〉 〈p〉Author(s): Shen Kang, Jianan Wang, Chaoyong Li, Jiayuan Shan〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉This paper presents an optimal solution to asteroid soft landing problem, on the base of 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si3.gif" overflow="scroll"〉〈mrow〉〈mi〉θ〈/mi〉〈mo〉−〈/mo〉〈mi〉D〈/mi〉〈/mrow〉〈/math〉 control technique and disturbance rejection mechanism. The control objective is to drive a probe to reach the surface of an asteroid with a desirable line-of-sight angle and zero velocity, eliminating the influence of external disturbance. Firstly, elementary 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si3.gif" overflow="scroll"〉〈mrow〉〈mi〉θ〈/mi〉〈mo〉−〈/mo〉〈mi〉D〈/mi〉〈/mrow〉〈/math〉 technique is applied in the absence of disturbance to tackle the nonlinear optimal control problem. Secondly, the disturbance is estimated in the fast-estimation framework with explicitly bounded estimation error. Afterwards, an integrated control protocol is presented in a feed-forward structure by the aid of an additional variable-structure term to ensure stability under time-varying disturbance. Simulation results of the proposed approach compared with the results of elementary 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si3.gif" overflow="scroll"〉〈mrow〉〈mi〉θ〈/mi〉〈mo〉−〈/mo〉〈mi〉D〈/mi〉〈/mrow〉〈/math〉 method and robust 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si3.gif" overflow="scroll"〉〈mrow〉〈mi〉θ〈/mi〉〈mo〉−〈/mo〉〈mi〉D〈/mi〉〈/mrow〉〈/math〉 method are presented at the end of this paper, demonstrating the effectiveness of the proposed control protocol.〈/p〉〈/div〉

Description: 〈p〉Publication date: November 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of the Franklin Institute, Volume 355, Issue 17〈/p〉 〈p〉Author(s): Xiangwei Bu, Guangjun He, Daozhi Wei〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉Though traditional prescribed performance control (PPC) schemes can guarantee tracking errors with desired transient performance, they cannot ensure the convergence of tracking errors with small overshoot. In this study, we propose a novel PPC methodology for a class of uncertain nonlinear dynamic systems based on back-stepping, guaranteeing output tracking with small (even zero) overshoot. Firstly, new performance functions are constructed to constrain tracking errors. Then, to facilitate control designs, the “constrained” systems are transformed into equivalent “unconstrained” ones by designing a series of transformed errors. Furthermore, robust back-stepping controllers, requiring no priori knowledge of uncertainties’ upper bounds, are developed utilizing transformed errors instead of initial tracking errors. Semi-globally uniformly bounded stability of the closed-loop control system is guaranteed via Lyapunov synthesis. Finally, simulation and experiment results are presented to verify the design.〈/p〉〈/div〉

Description: 〈p〉Publication date: November 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of the Franklin Institute, Volume 355, Issue 16〈/p〉 〈p〉Author(s): Fatim Zahra Ait Bella, Mohammed El Rhabi, Abdelilah Hakim, Amine Laghrib〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉In this paper, we investigate two new reflectance and illumination decomposition models based on a nonlocal partial differential equation (PDE) applied to text images. Taking into consideration the higher regularity level of the illumination compared to the reflectance, we propose a nonlocal PDE which deals with repetitive structures and textures that characterize the text image much better compared to the classical local PDEs. The aim of this approach is to use the repetitive features of the reflectance to efficiently extract it from the non-uniform illumination. This idea is motivated by extending the range of application of the nonlocal operators to such a problem. Numerical experiments on both grayscale and color text images show the performance and strength of the proposed nonlocal PDE.〈/p〉〈/div〉

Description: 〈p〉Publication date: October 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of the Franklin Institute, Volume 355, Issue 15〈/p〉 〈p〉Author(s): Saba Sedghizadeh, Soosan Beheshti〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉Data-driven Subspace Predictive Control (SPC) is an advanced model-free process control strategy in the presence of system constraints. Efficient implementation of SPC requires appropriate tuning of the controller horizons, which are called Prediction Horizon and Control Horizon. This tuning is a critical step to guarantee the SPC closed-loop stability and to enhance the closed-loop performance and robustness. In this paper we propose an optimal tuning method for unconstrained SPC, which can guarantee stability, computational efficiency and optimality of the unconstrained SPC closed-loop system and is applicable to non-minimum phase open-loop stable or marginally stable systems. Derivation of general form of closed-loop transfer function for unconstrained SPC, and providing a necessary and sufficient condition of the closed-loop stability is the primary contribution of this work. In addition, the stability analysis enabled us to propose an algorithm to determine the shortest-feasible-prediction-horizon and the feasible range of prediction horizon. Consequently, these results are used in proposing a new algorithm to determine the SPC horizons in optimal manner. Simulation results illustrate effectiveness and importance of our proposed stability analysis and horizons tuning algorithm for unconstrained SPC.〈/p〉〈/div〉

Description: 〈p〉Publication date: November 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of the Franklin Institute, Volume 355, Issue 17〈/p〉 〈p〉Author(s): Miao Yu, Jian chang Liu〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉A method for nuclear norm-based recursive subspace prediction of time-varying continuous-time stochastic systems via distribution theory is proposed. The random distribution theory is adopted to describe the time-derivative of stochastic processes, which is the key to obtain the input–output algebraic equation. The low-rank matrix approximation of the input–output projection matrix is established by nuclear norm minimization instead of the singular value decomposition. Moreover, the optimization problem is deduced by the alternating direction method of multipliers. According to the angle rotation between past and present subspaces spanned by the extended observability matrices, the future signal subspace is predicted by the present subspace. Further, the system matrices are predicted and the corresponding system model is obtained. The results of simulation studies show the effectiveness of the presented method.〈/p〉〈/div〉

Description: 〈p〉Publication date: November 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of the Franklin Institute, Volume 355, Issue 17〈/p〉 〈p〉Author(s): Wenjie Si, Xunde Dong〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉Decentralized adaptive neural backstepping control scheme is developed for uncertain high-order stochastic nonlinear systems with unknown interconnected nonlinearity and output constraints. For the control of high-order nonlinear interconnected systems, it is assumed that nonlinear system functions are unknown. It is for the first time to control stochastic nonlinear high-order systems with output constraints. Firstly, by constructing barrier Lyapunov functions, output constraints are handled. Secondly, at each recursive step, only one adaptive parameter is updated to overcome over-parameterization problems, and RBF neural networks are used to identify unknown nonlinear functions so that the difficulties caused by completely unknown system functions and stochastic disturbances are tackled. Finally, based on the Lyapunov stability method, the decentralized adaptive control scheme via neural networks approximator is proposed, ultimately reducing the number of learning parameters. It is shown that the designed controller can guarantee all the signals of the resulting closed-loop system to be semi-globally uniformly ultimately bounded (SGUUB), and the tracking errors for each subsystem are driven to a small neighborhood of zero. The simulation studies are performed to verify the effectiveness of the proposed control strategy.〈/p〉〈/div〉

Description: 〈p〉Publication date: November 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of the Franklin Institute, Volume 355, Issue 17〈/p〉 〈p〉Author(s): Yawu Wang, Xuzhi Lai, Pan Zhang, Min Wu〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉This paper presents an adaptive robust control strategy based on a radial basis function neural network (RBFNN) and an online iterative correction method (OICM) for a planar 〈em〉n〈/em〉-link underactuated manipulator with a passive first joint to realize its position control objective. An uncertain model of the planar 〈em〉n〈/em〉-link underactuated manipulator is built, which contains the parameter perturbation and the external disturbance. The adaptive robust controllers based on the RBFNN are designed to realize the model reduction, which makes the system reduce to a planar virtual three-link underactuated manipulator (PVTUM) and simplifies the complexity of the system control. An online differential evolution (DE) algorithm is used to calculate the target angles of the PVTUM based on the nominal model parameters. The control of the PVTUM is divided into two stages, and the adaptive robust controllers are still employed to realize the control objective of each stage. Then, the OICM is used to correct the deviations of all link angles of the PVTUM caused by the parameter perturbation, which makes the end-point of the system gradually approach to its target position. Finally, simulation results of a planar four-link underactuated manipulator demonstrate the effectiveness of the proposed adaptive robust control strategy.〈/p〉〈/div〉

Description: 〈p〉Publication date: January 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of the Franklin Institute, Volume 356, Issue 1〈/p〉 〈p〉Author(s): Ali Abooee, Mohammad Mehdi Arefi〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉In this paper, the robust finite-time stabilization problem for a fully suspended five-degree-of-freedom active magnetic bearing system is addressed in the presence of external disturbances and additive uncertainties. By developing the nonsingular terminal sliding mode control and defining new nonlinear sliding surfaces, three separate classes of stabilizers are proposed to regulate and place the suspended rotor in the desired positions of air gaps within adjustable finite times. The suggested nonlinear sliding surfaces and designed control inputs for each class of stabilizers are two major differences between these stabilizers. It is mathematically proven that five control voltages of this system, designed by each class of the suggested stabilizers, are able to locate the suspended rotor at the centers of air gaps in the adjustable finite time which is summation of two reaching and settling finite times. Moreover, several new inequalities are extracted for determining the reaching and settling finite times related to the three classes of stabilizers. These inequalities reveal the dependencies between optional parameters of the proposed stabilizers and the mentioned finite times. Finally, numerical simulations are provided to illustrate the efficiency and good performance of each class of the designed stabilizers.〈/p〉〈/div〉

Description: 〈p〉Publication date: November 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of the Franklin Institute, Volume 355, Issue 17〈/p〉 〈p〉Author(s): Zhaolu Tian, C.M. Fan, Youjun Deng, P.H. Wen〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉In this paper, based on the Smith iteration (Smith, 1968), an inner-outer (IO) iteration algorithm for solving the coupled Lyapunov matrix equations (CLMEs) is presented. First, the IO iteration algorithm for solving the Sylvester matrix equation is proposed, and its convergence is analyzed in detail. Second, the IO iteration algorithm for solving the CLMEs is constructed. By utilizing the latest estimation, a current-estimation-based and two weighted IO iteration algorithms are also given for solving the CLMEs, respectively. Convergence analyses indicate that the iteration solutions generated by these algorithms always converge to the unique solutions to the CLMEs for any initial conditions. Finally, Several numerical examples are provided to show the superiority of the proposed numerical algorithms.〈/p〉〈/div〉

Description: 〈p〉Publication date: October 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of the Franklin Institute, Volume 355, Issue 15〈/p〉 〈p〉Author(s): Lingling Lv, Zhe Zhang, Lei Zhang, Xianxing Liu〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉The paper is dedicated to solving the generalized periodic discrete-time coupled Sylvester matrix equation, which is frequently encountered in control theory and applied mathematics. The solvable condition and a iterative algorithm for this equation are presented. The proposed method is developed from a point of least squares method. The rationality of the method is testified by theoretical analysis, which shows that the algorithm can solve the problem within finite number of iterations. The presented approach is numerically reliable and requires less computation. A numerical example illustrates the effectiveness of the raised result.〈/p〉〈/div〉

Description: 〈p〉Publication date: November 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of the Franklin Institute, Volume 355, Issue 17〈/p〉 〈p〉Author(s): Eva Gyurkovics, Krisztina Kiss, Ali Kazemy〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉This paper is devoted to the non-fragile exponential synchronization problem of complex dynamical networks with time-varying coupling delays via sampled-data static output-feedback controller involving a constant signal transmission delay. The dynamics of the nodes contain s quadratically restricted nonlinearities, and the feedback gain is allowed to have norm-bounded time-varying uncertainty. The control design is based on a Lyapunov–Krasovskii functional, which consists of the sum of terms assigned to the individual nodes, i.e., it is constructed without merging the complex dynamical network’s nodes into a single large-scale system. In this way, the proposed design method has substantially reduced computational complexity and improved conservativeness, and guaranties non-fragile exponential stability of the error system. The sufficient stability condition is expressed in terms of linear matrix inequalities that are solvable by standard tools. The efficiency of the proposed method is illustrated by numerical examples.〈/p〉〈/div〉

Description: 〈p〉Publication date: October 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of the Franklin Institute, Volume 355, Issue 15〈/p〉 〈p〉Author(s): Liqian Dou, Jingqi Gao, Qun Zong, Zhengtao Ding〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉In this paper, a multi-model switching control is developed for air-breathing hypersonic vehicle with variable geometry inlet(AHV-VGI). A variable geometry inlet with the translating cowl is adopted to capture the enough air mass flow for the scramjet engine, which can ensure a more powerful thrust. However, the using of VGI causes the unknown changes of the aerodynamics and thrust, making the model of AHV more complex. Therefore, we firstly analyze the thrust characteristic with the translating cowl and present the conception of optimal elongation distance of translating cowl(EDTC). Consequently, multiple different nonlinear aerodynamic models are constructed by curve fitting for each position of the translating cowl. Then, a switching mechanism dependent on EDTC is proposed and the adaptive RBF neural controllers are designed for velocity subsystem and altitude system of every model. Furthermore, the common Lyapunov functional is constructed to prove the stability of the multi-model switching process. Finally, numerical simulations are given to demonstrate the effectiveness of the proposed control approach for AHV-VGI.〈/p〉〈/div〉

Description: 〈p〉Publication date: November 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of the Franklin Institute, Volume 355, Issue 16〈/p〉 〈p〉Author(s): Qun Liu, Daqing Jiang, Tasawar Hayat, Ahmed Alsaedi〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉In this paper, we propose and study a stochastic predator–prey model with herd behavior. Firstly, by constructing a suitable stochastic Lyapunov function, we establish sufficient conditions for the existence and uniqueness of an ergodic stationary distribution of the positive solutions to the model. Then we establish sufficient conditions for extinction of the predator population in two cases, that is, the first case is the prey population survival and the predator population extinction; the second case is all the prey and predator populations extinction. Finally, some examples together with numerical simulations are introduced to illustrate the theoretical results.〈/p〉〈/div〉

Description: 〈p〉Publication date: October 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of the Franklin Institute, Volume 355, Issue 15〈/p〉 〈p〉Author(s): Zhibo Wang, Huaiqin Wu〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉This paper is concerned with the global projective synchronization in fixed time for complex dynamical networks (CDNs) with nonidentical nodes in the presence of disturbances. Firstly, in order to realize the fixed-time projective synchronization of CDNs with matched disturbances, the second-order sliding mode is established, and the global fixed-time reachability of sliding manifolds is analyzed. The fixed-time stability of the sliding mode dynamics is also proved analytically based on Lyapunov stability theory. Moreover, the fixed convergence time of both reaching and sliding mode phases can be adjusted to any desired values in advance by the choice of the designable parameters. Secondly, in order to realize the fixed-time projective synchronization of CDNs with mismatched disturbances, a super-twisting-like (STL) controller, which does not require the information of the derivative of the sliding variable, is designed, and the synchronization condition is addressed in terms of linear matrix inequalities (LMIs). By the proposed controllers, continuous control signals can be provided to reduce the chattering effect and improve the control accuracy. Finally, two numerical examples are given to demonstrate the validity of the theoretical results and the the feasibility of the proposed approaches.〈/p〉〈/div〉

Description: 〈p〉Publication date: November 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of the Franklin Institute, Volume 355, Issue 17〈/p〉 〈p〉Author(s): Jiange Wang, Xiaoyuan Luo, Xiaolei Li, Xinping Guan〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉In this paper, the specified-time bearing-based formation control problem is investigated via a dynamic gain approach. Both the leader-follower and leaderless cases for single- and double-integral multi-agent systems are considered with bearing measurement, respectively. By considering the communication graph as bearing rigid, distributed bearing-based controllers with a time-varying gain are designed. By using time transformation method and Lyapunov stability theory, the close-loop systems under the proposed protocols can achieve the target formation within the specified time. Comparing with some existing results, the proposed approaches can make multi-agent systems converge to the desired formation within any preset time without dependence on the initial conditions or system parameters. Finally, some simulations and experiments are presented to demonstrate the effectiveness of the proposed algorithms.〈/p〉〈/div〉

Description: 〈p〉Publication date: November 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of the Franklin Institute, Volume 355, Issue 17〈/p〉 〈p〉Author(s): Ali Sghaier Tlili〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉This study investigates the problem of robust tracking control for interconnected nonlinear systems affected by uncertainties and external disturbances. The designed 〈em〉H〈/em〉〈sub〉∞〈/sub〉 dynamic output-feedback model reference tracking controller is parameterized in terms of linear matrix inequalities (LMIs), which is formulated within a convex optimization problem readily implementable. The resolution of such a problem, guarantying not only the quadratic stability but also a prescribed performance level of the resulting closed-loop system, enables to calculate concurrently the robust decentralized control and observation gain matrices. The established LMI conditions are computed in a single-step resolution to obtain all the controller/observer parameters and therefore to overcome the problem of iterative algorithm based on a multi-stage resolution leading in most cases to conservative and suboptimal solutions. Numerical simulations on diverse applications ranging from a numerical academic example to coupled inverted double pendulums and a 3-strongly interconnected machine power system are provided to corroborate the merit of the proposed control scheme.〈/p〉〈/div〉

Description: 〈p〉Publication date: November 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of the Franklin Institute, Volume 355, Issue 17〈/p〉 〈p〉Author(s): Tao Wu, Lianglin Xiong, Jinde Cao, Zixin Liu, Haiyang Zhang〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉This paper discusses the stabilization criteria for stochastic neural networks of neutral type with both Markovian jump parameters. First, delay-dependent conditions to guarantee the globally exponential stability in mean square and almost surely exponential stability of such systems are obtained by combining an appropriate constructed Lyapunov–Krasovskii functional with the semi-martingale convergence theorem. These conditions are in terms of the linear matrix inequalities (LMIs), which can be some less conservative than some existing results. Second, based on the obtained stability conditions, the state feedback controller is designed. Finally, four numerical examples are provided to illustrate the effectiveness and significant improvement of the proposed method.〈/p〉〈/div〉

Description: 〈p〉Publication date: November 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of the Franklin Institute, Volume 355, Issue 17〈/p〉 〈p〉Author(s): Yuusuke Kobayashi, Takahiro Endo, Fumitoshi Matsuno〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉This paper discusses formation problem for robotic swarms when multiple robotic swarms cross one another's path. To realize the crossing motion, collision avoidance between agents is an important issue, with the potential to cause a general mix-up of formation during the crossing motion. To realize an orderly and well-organized crossing motion with the least mix-up, as well as collision avoidance, we propose a distributed controller. This well-organized crossing motion can realize visually appealing and highly entertaining robotic mass games. This paper proposes a distributed controller using the gradient of the cost functions about the formation maintenance, collision avoidance, and tracking to the desired trajectory. We then prove that we can achieve a well-organized crossing motion of multiple robotic swarms under several assumptions. Finally, experimental and numerical simulations are carried out to investigate whether the well-organized crossing motion can be achieved.〈/p〉〈/div〉

Description: 〈p〉Publication date: November 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of the Franklin Institute, Volume 355, Issue 17〈/p〉 〈p〉Author(s): Xu-Guang Li, Jun-Xiu Chen, Silviu-Iulian Niculescu, Arben Çela〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉Most of the reported Lotka–Volterra examples have at most one stability interval for the delay parameters. Furthermore, the existing methods fall short in treating more general case studies. Inspired by some recent results for analyzing the stability of time-delay systems, this paper focuses on a deeper characterization of the stability of Lotka–Volterra systems w.r.t. the delay parameters. More precisely, we will introduce the recently-proposed frequency-sweeping approach to study the complete stability problem for a broad class of linearized Lotka–Volterra systems. As a result, the whole stability delay-set can be analytically determined. Moreover, as a significant byproduct of the proposed approach, some Lotka–Volterra examples are found to have multiple stability delay-intervals. To the best of the authors’ knowledge, such a characterization represents a novelty for having some insights in the population dynamics: in some situations, a longer maturation period of species is helpful for the stability of a population system.〈/p〉〈/div〉

Description: 〈p〉Publication date: October 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of the Franklin Institute, Volume 355, Issue 15〈/p〉 〈p〉Author(s): Lijuan Liu, Yan Wang, Cheng Wang, Feng Ding, Tasawar Hayat〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉This paper focuses on the parameter estimation problems of multivariate equation-error systems. A recursive generalized extended least squares algorithm is presented as a comparison. Based on the maximum likelihood principle and the coupling identification concept, the multivariate equation-error system is decomposed into several regressive identification models, each of which has only a parameter vector, and a coupled subsystem maximum likelihood recursive least squares identification algorithm is developed for estimating the parameter vectors of these submodels. The simulation example shows that the proposed algorithm is effective and has high estimation accuracy.〈/p〉〈/div〉

Description: 〈p〉Publication date: October 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of the Franklin Institute, Volume 355, Issue 15〈/p〉 〈p〉Author(s): Xing Fang, Fei Liu, Zhengtao Ding〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉In this paper, a novel robust control strategy based on disturbance-compensation-gain (DCG) construction approach is proposed for small-scale unmanned helicopters in the presence of high-order mismatched disturbances. The overall control structure consists of two hierarchical layers. The inner-loop controller is to guarantee the stability of the unmanned helicopters subject to high-order mismatched disturbances. With the estimation of the disturbances and their successive derivatives via finite-time disturbance observer (FTDO), by properly designing some disturbance compensation gains, a novel robust controller is developed to remove the high-order mismatched disturbances from the output channels. The outer-loop controller is to produce flight commands for inner-loop system, as well as to track the reference trajectory, which is carried out with the dynamic inversion technique. The simulation results demonstrate that the unmanned helicopters are capable to perform flight missions autonomously with the proposed control strategy.〈/p〉〈/div〉

Description: 〈p〉Publication date: October 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of the Franklin Institute, Volume 355, Issue 15〈/p〉 〈p〉Author(s): Yushu Yu, Xilun Ding〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉The dynamics of multi-DOF aerial manipulators is complex system evolving in non-Euclidean Lie group, making design and tuning of the control of such systems challenge. In this paper we consider the nonlinear geometric control for aerial manipulation system. The linearized tracking error kinematic equation of motion on SO(3) is obtained from the variation on SO(3). Based on the linearized tracking error kinematic equation of motion on SO(3), the trajectory linearization control for the kinematics on SO(3) is investigated. The decoupled dynamics of multi-DOF aerial manipulator enables us to apply the results of trajectory linearization control for the kinematics on SO(3). We then design the entire controller for aerial manipulation system by composing different trajectory linearization control loops. Such controller structure eases the controller implementation and tuning procedure. The stability of the proposed controlled system is analyzed using Lyapunov’s method. The proof is finished from inner loop to outer loop. It is proven that the closed loop shape system is exponentially stable. The attraction basin of the configuration error for the shape system can almost cover the whole 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si3.gif" overflow="scroll"〉〈mrow〉〈mtext〉SO〈/mtext〉〈mrow〉〈mo〉(〈/mo〉〈mn〉3〈/mn〉〈mo〉)〈/mo〉〈/mrow〉〈mo〉×〈/mo〉〈msup〉〈mi mathvariant="double-struck"〉R〈/mi〉〈mi〉n〈/mi〉〈/msup〉〈/mrow〉〈/math〉. The stability of the system considering the actuator dynamics and perturbations is also discussed in this paper. From the stability of the shape system, the stability of the entire system is proven. The stability analysis results are further verified through several numerical simulations.〈/p〉〈/div〉

Description: 〈p〉Publication date: January 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of the Franklin Institute, Volume 356, Issue 1〈/p〉 〈p〉Author(s): Tairen Sun, Yongping Pan〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉This paper proposes a robust adaptive control strategy for a class of state-constrained uncertain nonlinear systems with prescribed transient and steady-state behavior. The prescribed tracking performance can be characterized by constraints on an output tracking error. Both state and output constraints are achieved by bounding integral barrier Lyapunov functions in the backstepping procedure. A robust adaptive term is designed to compress auxiliary system uncertainties without the knowledge of their bounds. The satisfaction of control constraints and tracking error convergence are verified by theoretical analysis and are illustrated by simulation results.〈/p〉〈/div〉

Description: 〈p〉Publication date: November 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of the Franklin Institute, Volume 355, Issue 17〈/p〉 〈p〉Author(s): Dianqiang Li, Pei Cheng, Mingang Hua, Fengqi Yao〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉In this paper, by using Lyapunov functions, Razumikhin techniques and stochastic analysis approaches, the robust exponential stability of a class of uncertain impulsive stochastic neural networks with delayed impulses is investigated. The obtained results show that delayed impulses can make contribution to the stability of system. Compared with existing results on related problems, this work improves and complements ones from some works. Two examples are discussed to illustrate the effectiveness and the advantages of the results obtained.〈/p〉〈/div〉