Takagi–Sugeno Model Based Event-Triggered Fuzzy Sliding-Mode Control of Networked Control Systems With Semi-Markovian Switchings

Summary This paper studies the event‐triggered H∞ control for synchronization of networked switched master‐slave systems under external disturbance, stochastic attacks, and quantization. With the proposed event‐triggering schemes, the communication frequency and data packets can be effectively regulated and reduced. To reduce further the burden of network transmission, the quantized control is applied. Moreover, the network transmission delay and the stochastic cyberattacks are concerned. In addition, the synchronization problem between switched master systems and switched slave systems is transformed into a stability problem of switched error systems. By adopting multiple Lyapunov functions and average dwell time method, sufficient conditions are constructed to assure the mean‐square exponential stability with H∞ performance of the switched error systems. Meanwhile, the stagger between data switching instants and triggering instants is discussed in the system in detail. Accordingly, the controller gains and event‐triggering parameters are obtained utilizing a set of linear matrix inequalities. Finally, a numerical simulation and a practical example are illustrated to demonstrate the effectiveness of the presented method.

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“…Proof. Denoting the left side of inequality (19) as 1i , then taking apart the matrix, it can be obtained that…”

Section: Case 2: the Switching Intervalmentioning

confidence: 99%

Event‐triggered H_∞ synchronization control for switched master‐slave systems subject to stochastic cyber attacks and quantization

Liu

Qiu

et al. 2020

Optim Control Appl Methods

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“…Then, it was computed that

ℰ {π_{i j} (h)} = \int_{0}^{\infty} π_{i j} (h) g_{i} (h) d h

, where g i ( h ) is the PDF of the sojourn‐time h staying at mode i . Therefore, the mathematical expectation of the TR matrix can be defined by

[\begin{array}{llll} ℰ false{π_{11} false(h false) false} & ℰ false{π_{12} false(h false) false} & \dots & ℰ false{π_{1 n} false(h false) false} \\ ℰ false{π_{21} false(h false) false} & ℰ false{π_{22} false(h false) false} & \dots & ℰ false{π_{2 n} false(h false) false} \\ ⋮ & ⋮ & ⋱ & ⋮ \\ ℰ false{π_{n 1} false(h false) false} & ℰ false{π_{n 2} false(h false) false} & \dots & ℰ false{π_{n n} false(h false) false} \end{array}] .

(d): In view of the above three cases, which all need partial or full information on the TR π ij ( h ), the following TR matrix in is introduced to better accommodate practical dynamical systems:

[\begin{array}{llll} π_{11} + normalΔ π_{11} false(h false) & ? & \dots & π_{13} + normalΔ π_{13} false(h false) \\ ? \end{array}]

…”

Section: Problem Formulation and Preliminariesmentioning

confidence: 99%

“…However, it is noted that all the results proposed in the above literature studies require information on all TRs π ij ( h ), either full or partial cases. Recently, new results are proposed in Reference with a novel method to deal with generally uncertain time‐varying TRs, that is, some TRs are fully unknown. But in Reference , only two cases for the mode information in the TR matrix are investigated, which is far from enough since some important and difficult issues have not touched yet, especially for the types that TRs from one mode to another are totally unknown.…”

Section: Introductionmentioning

confidence: 99%

“…Recently, new results are proposed in Reference with a novel method to deal with generally uncertain time‐varying TRs, that is, some TRs are fully unknown. But in Reference , only two cases for the mode information in the TR matrix are investigated, which is far from enough since some important and difficult issues have not touched yet, especially for the types that TRs from one mode to another are totally unknown. Although some methods have been proposed in dealing with MJLSs with deficiency mode information, the techniques cannot be extended to S‐MJLSs directly or might be invalid for S‐MJLSs.…”

Section: Introductionmentioning

confidence: 99%

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Further criterion for stochastic stability analysis of semi‐Markovian jump linear systems

Jiang

Karimi

2020

Intl J Robust & Nonlinear

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This article is devoted to provide further criterion for stochastic stability analysis of semi-Markovian jump linear systems (S-MJLSs), in which more generic transition rates (TRs) will be studied. As is known, the time-varying TR is one of the key issues to be considered in the analysis of S-MJLS. Therefore, this article is to investigate general cases for the TRs that covered almost all types, especially for the type that the jumping information from one mode to another is fully unknown, which is merely investigated before. By virtue of stochastic functional theory, sufficient conditions are developed to check stochastic stability of the underlying systems via linear matrix inequalities formulation combined with a maximum optimization algorithm. Finally, a numerical example is given to verify the validity and effectiveness of the obtained results. K E Y W O R D Slinear matrix inequalities, semi-Markovian jump systems, stochastic stability, uncertain transition rates INTRODUCTIONThe semi-Markovian jump linear systems (S-MJLSs) 1 have received considerable attention in the recent control theory literature due to their better reflection of physical systems than Markovian jump linear systems (MJLSs). Traditionally, the MJLSs are applied to model physical systems with abrupt structure changes 2-6 with great efficiency, but with high demand for accuracy of modeling physical systems nowadays, the MJLS approach apparently shows its limitations, which mainly derives from its sojourn-time h follows a memory-less exponential distribution. In a continuous-time S-MJLS, the sojourn-time h follows more general continuous probability distributions, such as the Weibull distribution, rather than confined to the exponential distribution in MJLSs. The consequence is that the transition rates (TRs) in S-MJLSs are relaxed from constant to sojourn-time dependent time-varying parameters ij (h). Due to the general property of S-MJLSs, the problems of stochastic stability analysis, stabilization, and filtering of S-MJLSs are particularly becoming hot topics in the literature. For example, the robust stochastic stability and the control design problems for S-MJLSs were studied in References 7-9. The concern on the stochastic stability and stabilization for a class of discrete-time S-MJLSs was dealt with in References 10 and 11. The observer-based sliding mode approach was proposed for stabilization of S-MJLSs in References 12-14. The ℒ ∞ control for positive delay systems with semi-Markov process was stuided in Reference 15. The Takagi-Sugeno model approach was introduced to fuzzy control of nonlinear single-link robot arm model with semi-Markov switching parameters in References 16 and 17, and for more details, please refer to References 18 and 19 and reference therein. Int J Robust Nonlinear Control. 2020;30:2689-2700. wileyonlinelibrary.com/journal/rnc

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“…The event-triggered control strategy is proposed to solve this problem and several results have been obtained. [16][17][18][19][20] Specifically, an event-triggered adaptive control for a class of nonlinear systems was considered in Reference 21 . Event-triggered adaptive backstepping control for parametric strict-feedback nonlinear systems was developed in Reference 22 .…”

Section: Introductionmentioning

confidence: 99%

Global adaptive finite‐time stabilization for a class of p‐normal nonlinear systems via an event‐triggered strategy

Guo

Xiang

2020

Intl J Robust & Nonlinear

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This article addresses the problem of global adaptive finite-time control for a class of p-normal nonlinear systems via an event-triggered strategy. A state feedback controller is first designed for the nominal system by adding a power integrator method. Then, by the skillful design of adaptive dynamic gain mechanism, a novel event-triggered controller is constructed for uncertain nonlinear system without homogeneous growth condition. It is proved that the global finite-time stabilization of p-normal nonlinear systems is guaranteed and the Zeno phenomenon is excluded. Finally, two examples are presented to indicate the effectiveness of the proposed control scheme. K E Y W O R D S p-normal nonlinear systems, adaptive control, event-triggered control, global finite-time stabilization 1 Int J Robust Nonlinear Control. 2020;30:4059-4074.wileyonlinelibrary.com/journal/rnc

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Takagi–Sugeno Model Based Event-Triggered Fuzzy Sliding-Mode Control of Networked Control Systems With Semi-Markovian Switchings

Cited by 184 publications

References 40 publications

Event‐triggered H_∞ synchronization control for switched master‐slave systems subject to stochastic cyber attacks and quantization

Event‐triggered H_∞ synchronization control for switched master‐slave systems subject to stochastic cyber attacks and quantization

Further criterion for stochastic stability analysis of semi‐Markovian jump linear systems

Global adaptive finite‐time stabilization for a class of p‐normal nonlinear systems via an event‐triggered strategy

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Takagi–Sugeno Model Based Event-Triggered Fuzzy Sliding-Mode Control of Networked Control Systems With Semi-Markovian Switchings

Cited by 184 publications

References 40 publications

Event‐triggered H∞ synchronization control for switched master‐slave systems subject to stochastic cyber attacks and quantization

Event‐triggered H∞ synchronization control for switched master‐slave systems subject to stochastic cyber attacks and quantization

Further criterion for stochastic stability analysis of semi‐Markovian jump linear systems

Global adaptive finite‐time stabilization for a class of p‐normal nonlinear systems via an event‐triggered strategy

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Event‐triggered H_∞ synchronization control for switched master‐slave systems subject to stochastic cyber attacks and quantization

Event‐triggered H_∞ synchronization control for switched master‐slave systems subject to stochastic cyber attacks and quantization