Adaptive sliding-mode-based control for stochastic nonlinear systems subject to probabilistic interval delay: A delay-fractioning method

Jia, Fengjiao; Hu, Jun; Feng, Lichao; Chen, Dongyan; Tan, Chong

doi:10.1016/j.jfranklin.2019.10.017

Cited by 8 publications

(4 citation statements)

References 41 publications

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“…Then, the proof is completed. Remark Considering the issue of balancing conservatism and computational complexity, we do not select the delay‐fractioning technique in [13] and [14] to construct Lyapunov–Krasovskii functionals. It is well known that the augmented Lyapunov–Krasovskii functionals can effectively reduce the conservatism of stability analysis.…”

Section: Resultsmentioning

confidence: 99%

“…Nevertheless, the derivatives of membership functions need to be bounded when the fuzzy Lyapunov-Krasovskii functional method is employed. Stability conditions of T-S fuzzy systems with time-varying delays were obtained by constructing novel Lyapunov-Krasovskii functionals dependent on the delay-fractioning technique in [13,14], where the conservatism could be reduced by increasing the segmentation step. However, while increasing the segmentation step, the delay-fractioning technique may introduce the larger decision variables and computational complexity.…”

Section: Introductionmentioning

confidence: 99%

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New relaxed stability and stabilization conditions for T‐S fuzzy systems with time‐varying delays

Zhou

Wang

2021

IET Control Theory & Appl

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This paper investigates the stability analysis and stabilization of T-S fuzzy systems with time-varying delays. First, a new augmented Lyapunov-Krasovskii functional is constructed, delay-dependent stability criteria in terms of linear matrix inequalities (LMIs) are obtained by combining them with the integral inequality technique and the reciprocally convex combination inequality. Based on the state space decomposition method, some piecewise membership functions are employed to approximate the membership functions. The piecewise membership functions can be locally represented in terms of the convex combinations of the supremum and infimum of some local basis functions. The boundary information of the membership functions is adequately taken into consideration in stability analysis, and then some relaxed membership-function-dependent stability results are obtained. Second, state feedback controllers for fuzzy systems with time-varying delays are presented under the imperfect premise-matching technique, whose membership functions and the number of fuzzy rules are allowed to be designed freely, consequently, the flexibility of controller design is improved. Finally, four numerical examples are given to demonstrate the effectiveness of the presented approaches.This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

New relaxed stability and stabilization conditions for T‐S fuzzy systems with time‐varying delays

Zhou

Wang

2021

IET Control Theory & Appl

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“…In Zhang et al (2018), a direct adaptive fuzzy backstepping controller is designed for a class of stochastic strict feedback systems which possess dynamic disturbances, unstructured uncertainties, and unmodeled dynamics. Since stochastic disturbances are inevitable in practical systems, therefore, several control techniques including sliding mode (Jia et al, 2020), Takagi-Sugeno (T-S) fuzzy (Wang and Yuan, 2021), and backstepping (Homayoun et al, 2020a) have been presented for stochastic non-linear systems. Among the existing methods, the capabilities of the backstepping controller in estimating unknown terms, uncertainties, and handling stochastic disturbances provide an interesting platform (Homayoun et al, 2020a).…”

Section: Introductionmentioning

confidence: 99%

Adaptive command-filtered finite-time control of non-strict feedback stochastic non-linear systems

Seifi

Sani

2022

Transactions of the Institute of Measurement and Control

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In this paper, an adaptive neural network (NN) finite-time command filter controller for a class of non-strict feedback stochastic non-linear systems has been investigated. Using error compensation signals and NNs, a command filter controller is presented which guarantees that all the signals of the closed-loop system are practical finite-time stable and the output signal tracks the given reference signal under the bounded error. In the design procedure, NNs are employed to approximate unknown non-linear functions, which contain all the state variables of the whole system, in order to avoid excessive and burdensome computations and ensure that the backstepping method works normally for non-strict feedback systems. Meanwhile, the “explosion of complexity” problem caused by the backstepping method is avoided using the command filter approach. The control scheme not only resolves the “explosion of complexity” problem but also eliminates the filtering error in finite-time. Finally, the simulation results are given to prove the effectiveness of the proposed control method.

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“…In Reference 16 the SMC stabilization of singular Markovian systems with classical Brownian motion has been studied with a stochastic sliding surface. There are other new works in this field; for instance see References 17–24 and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Mean square exponential stabilization of uncertain time‐delay stochastic systems with fractional Brownian motion

Parvizian

Khandani

2021

Intl J Robust & Nonlinear

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This article is concerned with exponential mean square stabilization of stochastic systems driven by fractional Brownian motion subject to state‐delay and uncertainties by sliding mode control. By applying the proposed method, the states of the system reach the sliding surface in finite time. Then, some sufficient conditions are given in terms of linear matrix inequalities (LMIs) to guarantee the mean‐square exponential stability of the sliding motion. The LMI conditions for mean‐square exponential stability of the sliding mode dynamics are derived by constructing a novel Lyapunov functional. Finally, a simulation example is presented which corroborates the accuracy of the results.

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Adaptive sliding-mode-based control for stochastic nonlinear systems subject to probabilistic interval delay: A delay-fractioning method

Cited by 8 publications

References 41 publications

New relaxed stability and stabilization conditions for T‐S fuzzy systems with time‐varying delays

New relaxed stability and stabilization conditions for T‐S fuzzy systems with time‐varying delays

Adaptive command-filtered finite-time control of non-strict feedback stochastic non-linear systems

Mean square exponential stabilization of uncertain time‐delay stochastic systems with fractional Brownian motion

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