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Journal ArticleDOI

Sliding mode control for semi-Markovian jump systems via output feedback

01 Jul 2017-Automatica (Pergamon)-Vol. 81, Iss: 81, pp 133-141
TL;DR: A sliding mode controller is synthesized to drive the underlying closed-loop system onto the sliding surface in finite time, locally for a given sliding region, which also guarantees the stochastic stability of sliding mode dynamical system.
About: This article is published in Automatica.The article was published on 2017-07-01. It has received 242 citations till now. The article focuses on the topics: Sliding mode control & State observer.
Citations
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Journal ArticleDOI
TL;DR: The observer-based adaptive sliding mode control (OBASMC) design for nonlinear uncertain singular semi-Markov jump systems satisfies the singular property and follows a stochastic semi- Markov process related to Weibull distribution.
Abstract: This paper deals with the observer-based adaptive sliding mode control (OBASMC) design for nonlinear uncertain singular semi-Markov jump systems. The system satisfies the singular property and follows a stochastic semi-Markov process related to Weibull distribution. Due to the influence of sensor factors in practical systems, the state vectors are not always known. Additionally, the unavoidable measurement errors in the actual system always lead to the model uncertainties and the unknown nonlinearity. Our attention is to design the OBASMC law for such a class of complex systems. First, by the use of the Lyapunov–Krasovskii functional, sufficient conditions are given, such that the sliding mode dynamics are stochastically admissible. Then, the OBASMC law is proposed to guarantee the reachability in a finite-time region. Finally, the practical system about dc motor model is given to verify the validity.

199 citations


Cites background from "Sliding mode control for semi-Marko..."

  • ...Furthermore, without taking the singularity into account, singular S-MJSs can be translated into nonsingular S-MJSs [21]–[23]....

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  • ...Remark 6: For the first question (Q1), different from nonsingular S-MJSs [21]–[23], we need to derive the weak infinitesimal operator from the point of view of probability distribution under the influence of singular factor (see formulas (17)-(20))....

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  • ...Therefore, the following three essential difficulties during the problem of OBASMC for nonlinear uncertain singular S-MJSs should be solved: Q1: Compared with nonsingular S-MJSs [21]–[23], how to derive the weak infinitesimal operator under the influence of singular factor? Q2: The controller gain matrices Ki in [9] cannot be solved directly....

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  • ...Second, the S-MJSs considered in [21]–[23] were nonsingular while the model in this paper is singular....

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Journal ArticleDOI
TL;DR: This paper studies the problems of stability and stabilization for a class of singular switching semi-Markovian jump systems and proposes a state feedback controller to ensure the unforced system to be regular, impulse-free, and exponentially mean-square stable.
Abstract: This paper studies the problems of stability and stabilization for a class of singular switching semi-Markovian jump systems. The general transition rates in the semi-Markov process cover completely unknown and uncertain bounded as two special cases. First, sufficient conditions are developed to ensure the unforced system to be regular, impulse-free, and exponentially mean-square stable. Then, by proposing a state feedback controller, sufficient conditions in terms of strict linear matrix inequalities are derived to guarantee the closed-loop system to be stochastically stabilziable. Finally, a numerical example is provided to show the effectiveness of the obtained results.

191 citations


Additional excerpts

  • ..., N2} with the following probability transition [31]: Pr{rt+ δ = j|rt = i, gt = α} = { π ij (h)δ + o(δ), i = j 1 + π ii (h)δ + o(δ), i = j where δ > 0 and limh→0 o(δ)/δ = 0, π ij (h) > 0(i = j) is the TR from mode i at time t to mode j at time t+ δ, and π ii (h) = −Σj = i π ij (h) < 0 for each i ∈ S2 , here, h represents the sojourn time....

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Journal ArticleDOI
TL;DR: This paper addresses the finite-time event-triggered control problem for nonlinear semi-Markovian switching cyber-physical systems (S-MSCPSs) under false data injection (FDI) attacks by using a mode-dependent piecewise Lyapunov-Krasovskii functional and some solvability conditions are established in light of a linear matrix inequality framework.
Abstract: This paper addresses the finite-time event-triggered control problem for nonlinear semi-Markovian switching cyber-physical systems (S-MSCPSs) under false data injection (FDI) attacks. Compared with the traditional time-triggered mechanism, the proposed event-triggered scheme (ETS) can effectively avoid network resource waste. Considering the network-induced delay in the modeling, a closed-loop system model with time delay is established in the unified framework. By the use of a mode-dependent piecewise Lyapunov-Krasovskii functional (LKF), stochastic finite-time stability (SFTS) criteria are established for the resultant closed-loop system. Then, some solvability conditions are established for the desired finite-time controller in light of a linear matrix inequality framework. Finally, an application example of vertical take-off and landing helicopter model (VTOLHM) is provided to demonstrate the effectiveness of the theoretical findings.

191 citations

Journal ArticleDOI
TL;DR: The proposed sliding mode control law is designed to attenuate the influences of uncertainty and nonlinear term in a finite-time region and the practical system about dc motor model is given to verify the validity of the proposed method.
Abstract: This paper deals with the problem of sliding mode control design for nonlinear stochastic singular semi-Markov jump systems (S-MJSs). Stochastic disturbance is first considered in studying S-MJSs with a stochastic semi-Markov process related to Weibull distribution. The specific information including the bound of nonlinearity is known for the control design. Our attention is to design sliding mode control law to attenuate the influences of uncertainty and nonlinear term. First, by the use of the Lyapunov function, a set of sufficient conditions are developed such that the closed-loop sliding mode dynamics are stochastically admissible. Then, the sliding mode control law is proposed to ensure the reachability in a finite-time region. Finally, the practical system about dc motor model is given to verify the validity of the proposed method.

135 citations


Cites background or methods from "Sliding mode control for semi-Marko..."

  • ...Therefore, some remarkable works about sliding mode control for MJSs and S-MJSs have attracted considerable attention [3], [7], [8], [10], [15]–[17], [22]–[24]....

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  • ...Fourth, the S-MJSs considered in [6]–[8] are nonsingular, whereas the model in this paper is singular....

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  • ...Remark 5: For the first question (Q1), different from S-MJSs without stochastic disturbance [5]–[12] and nonsingular S-MJSs [6]–[8], we need to derive the weak infinitesimal operator from the viewpoints of probability distribution by the use of Itô’s formula and Euler– Maruyama formula under the influences of singular factor and stochastic factor (see formulas (25)–(32) for some details)....

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  • ...Remark 4: Compared with nonsingular S-MJSs [6]–[8], there are some difficulties in considering singular property....

    [...]

  • ...Q1: Compared with S-MJSs [5]–[12] without stochastic disturbance and nonsingular S-MJSs [6]–[8], how to derive the weak infinitesimal operator under the influences of stochastic disturbance and singular factor? Q2: How to design the sliding mode control law so as to guarantee that the state responses of dynamic system can be driven onto the predefined sliding switching surfaces in finite time under the semiMarkov switching? The above aspects stimulate our research interests....

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Journal ArticleDOI
TL;DR: The main motivation for this paper is that the practical systems such as the communication network model (CNM) described by positive semi-Markov jump systems (S-MJSs) always need to consider the sudden change in the operating process.
Abstract: This paper deals with the problem of $\mathscr {L}_\infty$ control for positive delay systems with semi-Markov process. The system is subjected to a semi-Markov process that is time-varying, dependent on the sojourn time, and related to Weibull distribution. The main motivation for this paper is that the practical systems such as the communication network model (CNM) described by positive semi-Markov jump systems (S-MJSs) always need to consider the sudden change in the operating process. To deal with the corresponding problem, some criteria about stochastic stability and $\mathscr {L}_\infty$ boundedness are presented for the open-loop positive S-MJSs. Further, some necessary and sufficient conditions for state-feedback controller satisfying $\mathscr {L}_\infty$ boundedness and positivity of the resulting closed-loop system is established in standard linear programming. Finally, the practical system about the CNM is given to verify the validity of the proposed method.

130 citations


Cites background from "Sliding mode control for semi-Marko..."

  • ...Remark 6: As mentioned in [19], we have λ̄ij = ∫∞ 0 λ̄ij (h)fi(h)dh, where fi(h) is the probability distribution function of the ST h staying at mode i, which means that the range of the ST h is from 0 to ∞....

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  • ...It is noted that S-MJSs have gained particular research interests, such as stability [14]–[17], sliding mode control [18], [19], and quantized control [20]....

    [...]

References
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Book
01 Jan 1990
Abstract: This book is a monograph on hybrid parameter processes that are characterized by the presence of a discrete parameter and continuous variables. The author considers stochastic models in which the future control trajectories and the present solution do not determine completely the future of the system. The special stochastic processes and systems treated by the author are characterized by random transitions between different regimes, and this randomness primarily occurs through its discrete parameters. The book consists of eight chapters and two appendices. The appendices present brief summaries of basic probability, random processes, optima1 filtering, stochastic stability, stochastic maximum principles, matrix maximum principles, and stochastic dynamic programming. Readers might find it useful to consult references on applied probability and Markov processes before reading the eight chapters of this book. The first chapter introduces the reader to hybrid dynamic models by means of examples from target tracking, manufacturing processes, solar thermal receivers, and fault-tolerant control systems. Chapter 2 examines the global controllability and relative and stochastic stability of hybrid parameter systems. Also included in Chapter 2 are the concepts of Liapunov function and Liapunov exponents, observability, and detectability. Chapter 3 considers control optimization, jump linear quadratic regulators derived from maximum principles and dynamic programming, asymptotic behavior of quadratic regulators, suboptima1 solutions, optima1 switching output feedback, and algorithms for the optimization and evaluation of regulators for jump quadratic systems. The robustness, costs and their distribution, bound costs, and minimax solutions of jump linear systems are treated in Chapter 4, while the jump linear quadratic Gaussian problem is analyzed in some detail with Karman filtering and Poisson impulsive disturbances in Chapter 5. Optimal filtering, Wiener-driven oscillations, filter performance, and point-process observations are considered in Chapter 6. Chapter 7 deals with control under regime uncertainty, stability, control optimization, and regime estimation filters. The final chapter, Chapter 8, considers extensions of hybrid systems, non-Markovian processes, wide-band hybrid models, and extensions of the jump linear systems presented in the previous seven chapters. The book contains many theorems and proofs, is well illustrated with examples, and covers the material in depth. It is relatively free of typographical errors except that pages 206 and 207 have been interchanged.

917 citations

Journal ArticleDOI
TL;DR: In this paper, the authors studied stochastic stability properties in jump linear systems and the relationship among various moment and sample path stability properties, and showed that all second moment stability properties are equivalent and are sufficient for almost sure sample path stabilisation.
Abstract: Jump linear systems are defined as a family of linear systems with randomly jumping parameters (usually governed by a Markov jump process) and are used to model systems subject to failures or changes in structure. The authors study stochastic stability properties in jump linear systems and the relationship among various moment and sample path stability properties. It is shown that all second moment stability properties are equivalent and are sufficient for almost sure sample path stability, and a testable necessary and sufficient condition for second moment stability is derived. The Lyapunov exponent method for the study of almost sure sample stability is discussed, and a theorem which characterizes the Lyapunov exponents of jump linear systems is presented. Finally, for one-dimensional jump linear system, it is proved that the region for delta -moment stability is monotonically converging to the region for almost sure stability at delta down arrow 0/sup +/. >

731 citations

Journal ArticleDOI
TL;DR: Using Linear matrix inequalities (LMIs) approach, sufficient conditions are proposed to guarantee the stochastic stability of the underlying system and a reaching motion controller is designed such that the resulting closed-loop system can be driven onto the desired sliding surface in a limited time.
Abstract: In this note, we consider the problems of stochastic stability and sliding-mode control for a class of linear continuous-time systems with stochastic jumps, in which the jumping parameters are modeled as a continuous-time, discrete-state homogeneous Markov process with right continuous trajectories taking values in a finite set. By using Linear matrix inequalities (LMIs) approach, sufficient conditions are proposed to guarantee the stochastic stability of the underlying system. Then, a reaching motion controller is designed such that the resulting closed-loop system can be driven onto the desired sliding surface in a limited time. It has been shown that the sliding mode control problem for the Markovian jump systems is solvable if a set of coupled LMIs have solutions. A numerical example is given to show the potential of the proposed techniques.

613 citations

Journal ArticleDOI
TL;DR: A new necessary and sufficient condition is proposed in terms of strict linear matrix inequality (LMI), which guarantees the stochastic admissibility of the unforced Markovian jump singular system.
Abstract: This paper is concerned with the state estimation and sliding-mode control problems for continuous-time Markovian jump singular systems with unmeasured states. Firstly, a new necessary and sufficient condition is proposed in terms of strict linear matrix inequality (LMI), which guarantees the stochastic admissibility of the unforced Markovian jump singular system. Then, the sliding-mode control problem is considered by designing an integral sliding surface function. An observer is designed to estimate the system states, and a sliding-mode control scheme is synthesized for the reaching motion based on the state estimates. It is shown that the sliding mode in the estimation space can be attained in a finite time. Some conditions for the stochastic admissibility of the overall closed-loop system are derived. Finally, a numerical example is provided to illustrate the effectiveness of the proposed theory.

596 citations

Journal ArticleDOI
TL;DR: Improved delay-dependent stochastic stability and bounded real lemma (BRL) for Markovian delay systems are obtained by introducing some slack matrix variables and the conservatism caused by either model transformation or bounding techniques is reduced.
Abstract: This paper deals with the problems of delay-dependent robust Hinfin control and filtering for Markovian jump linear systems with norm-bounded parameter uncertainties and time-varying delays. In terms of linear matrix inequalities, improved delay-dependent stochastic stability and bounded real lemma (BRL) for Markovian delay systems are obtained by introducing some slack matrix variables. The conservatism caused by either model transformation or bounding techniques is reduced. Based on the proposed BRL, sufficient conditions for the solvability of the robust Hinfin control and Hinfin filtering problems are proposed, respectively. Dynamic output feedback controllers and full-order filters, which guarantee the resulting closed-loop system and the error system, respectively, to be stochastically stable and satisfy a prescribed Hinfin performance level for all delays no larger than a given upper bound, are constructed. Numerical examples are provided to demonstrate the reduced conservatism of the proposed results in this paper.

525 citations