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  • Articles  (72)
  • Oxford University Press  (72)
  • American Meteorological Society
  • Blackwell Publishing Ltd
  • Copernicus
  • Hindawi
  • Institute of Electrical and Electronics Engineers
  • Molecular Diversity Preservation International
  • Springer Nature
  • 2020-2022
  • 2010-2014  (72)
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  • 2012  (72)
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  • IMA Journal of Mathematical Control and Information  (31)
  • IMA Journal of Mathematical Control and Information. 2012; 29(3): 291-308. Published 2012 Jan 02. doi: 10.1093/imamci/dnr036.  (1)
  • IMA Journal of Mathematical Control and Information. 2012; 29(3): 343-356. Published 2012 Jan 29. doi: 10.1093/imamci/dnr044.  (1)
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  • Mathematics  (72)
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  • Articles  (72)
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  • Oxford University Press  (72)
  • American Meteorological Society
  • Blackwell Publishing Ltd
  • Copernicus
  • Hindawi
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  • 2020-2022
  • 2010-2014  (72)
  • 1990-1994
  • 1985-1989
  • 1960-1964
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  • Mathematics  (72)
  • 1
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    Lyapunov-based settling time estimate and tuning for twisting controller (2012)
    Oxford University Press
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    Publication Date: 2012-12-11
    Description: A novel switched control synthesis is developed and an upper bound on the settling time is obtained for a robust second-order sliding mode controller. The framework is based on step-by-step application of classical linear feedback design and the well-known ‘twisting’ controller. The underlying philosophy is to utilize globally exponentially stable linear feedback so that the trajectories enter an arbitrarily defined domain of attraction in finite time and then switch to the ‘twisting’ controller so that the trajectories settle at the origin in finite time. The proposed method is applied to the linear inverted pendulum to obtain an upper bound on the settling time of the closed-loop system in a full-state feedback setting in the presence of disturbances. Tuning rules to achieve the desired settling time are explicitly derived without recourse to the differential inequality of the Lyapunov function.
    Print ISSN: 0265-0754
    Electronic ISSN: 1471-6887
    Topics: Mathematics
    Published by Oxford University Press
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  • 2
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    Consensus of multi-agent systems on time scales (2012)
    Oxford University Press
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    Publication Date: 2012-12-11
    Description: This paper studies consensus problems of multi-agent systems over a directed network topology on time scales. Based on the theory of time scales, we discuss continuous-time and discrete-time consensus protocols under a unified framework by employing a Lyapunov-like technique. We find that consensus can be realized exponentially if the graininess function of the time scale is bounded and the coupling strength of the network is sufficiently small. Many existing results of both continuous-time and discrete-time consensus conditions are shown to be special cases of this paper. Moreover, our derived results contain both continuous-time and discrete-time cases simultaneously. Finally, several illustrative examples are presented to show the effectiveness of the theoretical results.
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    Electronic ISSN: 1471-6887
    Topics: Mathematics
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  • 3
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    Unified Lyapunov function for a finite-time stability analysis of relay second-order sliding mode control systems (2012)
    Oxford University Press
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    Publication Date: 2012-12-11
    Description: The paper deals with the problem of finite-time stability analysis of relay control systems described by ordinary differential equations and functional differential equations with discontinuous right-hand sides. It presents some extensions of Lyapunov theorems to this class of systems and discusses a method of an analytical construction of Lyapunov functions, which helps to design the unified Lyapunov function candidate for whole class of relay second-order sliding mode control systems. The theoretical results are supported by numerical simulations for systems with ‘twisting’, ‘nested’ and ‘suboptimal’ controllers.
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    Topics: Mathematics
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  • 4
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    Robust finite-time bounded observer design for a class of uncertain non-linear Markovian jump systems (2012)
    Oxford University Press
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    Publication Date: 2012-12-11
    Description: This paper concerns the state estimation problem for a class of uncertain non-linear Markovian jump systems, where the Markovian jump only occurs in some ‘short’ finite-time intervals. For this class of Markovian jump systems, the boundedness of estimation error deserves our investigation. By introducing the concepts of finite-time stochastic stability and boundedness, sufficient conditions ensuring uncertain non-linear Markovian jump system's finite-time stochastic stablility and boundedness are derived, then the result is extended to -disturbance attenuation case. Based on the analysis results, a robust observer ensuring the estimation error bounded with -disturbance attenuation in a prescribed boundary is constructed. A design algorithm is proposed when some parameter optimization is involved. Numerical design examples are given to illustrate the effectiveness of our results.
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    Electronic ISSN: 1471-6887
    Topics: Mathematics
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  • 5
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    Uniform sliding mode controllers and uniform sliding surfaces (2012)
    Oxford University Press
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    Publication Date: 2012-12-11
    Description: In this note, we propose two uniform sliding mode controllers (SMCs) for a second-order uncertain system. They provide convergence to an arbitrarily small vicinity centred at the origin in finite time, which can be bounded by some constant independent of the initial conditions and uncertainties. Towards this aim, a non-linear sliding surface is designed ensuring convergence, during the sliding motion, of every trajectory to an arbitrarily small vicinity of the origin in a finite time bounded by some constant, independent of the initial condition on the surface. A first-order SMC is designed providing convergence of every trajectory to the sliding surface in a finite time, bounded by another constant independent of the initial conditions and uncertainties/disturbances of a special class. In order to adjust chattering, a super twisting-based controller is suggested providing convergence of the trajectories to the sliding surface in a finite time bounded by some constant independent of any initial condition and uncertainties/disturbances of another class.
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    Topics: Mathematics
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  • 6
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    Assessing the exact stability region of the single-delay scalar equation via its Lyapunov function (2012)
    Oxford University Press
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    Publication Date: 2012-12-11
    Description: It is well known that one can determine the stability of a delay-free linear system either by verifying that all the roots of its characteristic polynomial are in the left half plane or by checking if the solution of the Lyapunov equation is positive definite. For linear systems with delays, many extensions of the first approach are reported in the literature. On the contrary, there exist no publications on extending the second approach to delay systems. In this note, it is shown that the second approach is possible for one of the simplest linear delay systems: stability conditions in terms of the Lyapunov function for the scalar delay equation, that match the frequency domain well-known result, are presented.
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    Topics: Mathematics
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  • 7
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    A Hilbert space extremum problem with application to multiple objective control system design (2012)
    Oxford University Press
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    Publication Date: 2012-12-11
    Description: Convex alternating projection algorithms (CAP) can be applied to solve multiple objective and hierarchical optimization problems in the area of control systems design involving both the H 2 and the H norms. The paper presents an application of a CAP algorithm for solving a simple problem in this area. This relies on the solution of an extremum problem in Hilbert space used to calculate a required projection onto a closed convex set.
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    Topics: Mathematics
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  • 8
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    On the Lyapunov-based second-order SMC design for some classes of distributed parameter systems (2012)
    Oxford University Press
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    Publication Date: 2012-12-11
    Description: This paper addresses the Lyapunov-based design of second-order sliding mode controllers in the domain of distributed parameter systems (DPSs). To the best of our knowledge, the recent authors’ publications (Orlov et al. , 2010, Continuous state-feedback tracking of an uncertain heat diffusion process. Syst. Control Lett. , 59 , 754–759; Orlov et al. , 2011, Exponential stabilization of the uncertain wave equation via distributed dynamic input extension. IEEE Trans. Autom. Control , 56 , 212–217; Pisano et al. , 2011, Tracking control of the uncertain heat and wave equation via power-fractional and sliding-mode techniques. SIAM J. Control Optim. , 49 , 363–382) represent the seminal applications of second-order sliding mode control techniques to DPSs. A Lyapunov-based framework of analysis was found to be appropriate in the above publications. While reviewing the main existing results in this new field of investigation, the paper provides the novelty as well and gives several hints and perspectives for the generalization, listing some open problems.
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  • 9
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    Adaptive fuzzy control for a class of non-linear systems (2012)
    Oxford University Press
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    Publication Date: 2012-12-11
    Description: This paper aims at exploring a fuzzy-based adaptive dynamic surface control (DSC) for a class of non-linear systems in strict-feedback form. Incorporating DSC technique into a fuzzy logic system based minimal-learning parameter algorithm and by introducing an initialization technique based on a surface error modification, it is shown that the design procedure and the computational burden can be greatly reduced and the L performance of system tracking error can be achieved. Besides, some restrictions on controlled systems in stability analysis of previous works are also removed. Simulation results are presented to demonstrate the efficiency of the proposed scheme.
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  • 10
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    One way for the probability of stability estimation of discrete systems with randomly chosen parameters (2012)
    Oxford University Press
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    Publication Date: 2012-09-06
    Description: In this paper, a simple effective and easy to implement method for the probability of stability estimation of the discrete systems with randomly chosen parameters is presented. Various formulas for different types of parameters’ distribution are obtained and used to calculate the probability of stability for an arbitrary-order system. The proposed method is illustrated on an example and its validity has been confirmed by the Monte Carlo method.
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    Topics: Mathematics
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