Adaptive tracking control for a class of random pure‐feedback nonlinear systems with Markovian switching

Yao, Liqiang; Zhang, Weihai

doi:10.1002/rnc.4071

Cited by 26 publications

(29 citation statements)

References 44 publications

(71 reference statements)

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“…This can be seen from the following two aspects. If

f_{i k} false(x false) = f_{i k} false({\overset{x}{true}}_{i} false)

{\overset{x}{true}}_{i} = {false[x_{1}, x_{2}, …, x_{i} false]}^{T}

, then system becomes a switched nonlinear system with strict feedback form in other works The control gains

{sans-serif g}_{k} false(x false) = 0

are allowed at some points.…”

Section: Problem Formulation and Preliminariesmentioning

confidence: 99%

“…Applying controllers (18) with the adaptive laws (19) and the switching law (17), we will achieve the global asymptotic stability of system (1) as shown in the following theorem, in which the notation and the constructive method are inspired by the book of Krstić et al 1 Theorem 1. Suppose that system (1) satisfies (3). If there exist constants > 0, l > 0 and functions kj (x) ≥ 0 with…”

Section: Adaptive Controllersmentioning

confidence: 99%

“…Typical and useful system structures include lower‐triangular structure and upper‐triangular structure, just to name a few. In particular, as a lower‐triangular structure, the strict‐feedback form has been extensively studied using the backstepping technique in the past decades . Especially, Long and Zhao investigated the problem of adaptive stabilization for a class of switched nonlinearly parameterized systems with the strict‐feedback form, where the solvability of the adaptive stabilization problem for subsystems is unnecessary.…”

Section: Introductionmentioning

confidence: 99%

“…In particular, as a lower-triangular structure, the strict-feedback form has been extensively studied using the backstepping technique in the past decades. [1][2][3][4][5][6][7][8][9][10][11] Especially, Long and Zhao 10 investigated the problem of adaptive stabilization for a class of switched nonlinearly parameterized systems with the strict-feedback form, where the solvability of the adaptive stabilization problem for subsystems is unnecessary. Based on the small-gain theorem, the global stabilization problem of switched nonlinear systems in strict-feedback form was studied in the work of Long et al 11 However, most real nonlinear systems do not admit triangular structure, such as a ball and beam system, 12 a continuously stirred tank reactor system.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Switched adaptive control for a class of switched nontriangular nonlinear systems with vanishing control gains

Xie

Yang

Zhao

2019

Intl J Robust & Nonlinear

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Summary In this paper, the adaptive control problem for a class of switched nontriangular nonlinear systems is investigated, which allows the control gains to vanish at some points. Neither the triangular structure nor the solvability of the adaptive control problem is required for each subsystem. A key point of this work is to solve the adaptive control problem of switched nontriangular nonlinear systems with vanishing control gains by the dual design of the controllers and switching signals. To this end, firstly, a hysteresis‐type control gains‐dependent switching law is designed, which makes the control gain of the active subsystem not vanish and thus the associated designed control input can enter into the active subsystem. Moreover, the designed switching law guarantees a dwell time between any adjacent switching instants, which rules out the Zeno behavior. Secondly, when the adaptive control problem of each subsystem is unsolvable, a sufficient condition ensuring the solvability of the adaptive control problem of switched nontriangular nonlinear systems is developed even if no control input can enter into subsystems at some points. Finally, the effectiveness of the proposed result is illustrated by two examples.

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“…This can be seen from the following two aspects. If

f_{i k} false(x false) = f_{i k} false({\overset{x}{true}}_{i} false)

{\overset{x}{true}}_{i} = {false[x_{1}, x_{2}, …, x_{i} false]}^{T}

, then system becomes a switched nonlinear system with strict feedback form in other works The control gains

{sans-serif g}_{k} false(x false) = 0

are allowed at some points.…”

Section: Problem Formulation and Preliminariesmentioning

confidence: 99%

Section: Adaptive Controllersmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Switched adaptive control for a class of switched nontriangular nonlinear systems with vanishing control gains

Xie

Yang

Zhao

2019

Intl J Robust & Nonlinear

View full text Add to dashboard Cite

show abstract

“…The researches on the stability of NNs, FOS, and stochastic systems have attracted the attention of a large number of researchers, and many achievements have been made [29][30][31][32][33][34][35][36][37][38][39][40][41]. The sliding mode control (SMC) is a very popular strategy for a general class of nonlinear uncertain systems, with a very large frame of applications fields.…”

Section: Introductionmentioning

confidence: 99%

Adaptive Synchronization for Uncertain Delayed Fractional-Order Hopfield Neural Networks via Fractional-Order Sliding Mode Control

Meng

Wang

2018

Mathematical Problems in Engineering

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Adaptive synchronization for a class of uncertain delayed fractional-order Hopfield neural networks (FOHNNs) with external disturbances is addressed in this paper. For the unknown parameters and external disturbances of the delayed FOHNNs, some adaptive estimations are designed. Firstly, a fractional-order switched sliding surface is proposed for the delayed FOHNNs. Then, according to the fractional-order extension of the Lyapunov stability criterion, a fractional-order sliding mode controller is constructed to guarantee that the synchronization error of the two uncertain delayed FOHNNs converges to an arbitrary small region of the origin. Finally, a numerical example of two-dimensional uncertain delayed FOHNNs is given to verify the effectiveness of the proposed method.

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Event‐triggered control for a class of nonlinear random systems involving time‐varying delay and exogenous disturbances

Zhang

Wang

et al. 2021

Asian Journal of Control

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In terms of system modeling, random differential equations (RDEs) with colored noise are demonstrated to be more appropriate than stochastic differential equations (SDEs) relating to white noise in most practical situations. This paper discusses a category of nonlinear random systems involving time‐varying delay and exogenous disturbances. The definitions for noise‐to‐state practically stable (NSPS) and noise‐to‐state practically exponentially mean‐square stable (NSPEMS) are first given. An event‐based controller is then constructed to render the closed‐loop system NSPEMS and circumvents the Zeno behavior at the same time. Since the introduction of event‐triggered mechanism endows the closed‐loop system with hybrid behaviors, event‐based control for RDE systems still remains difficult to deal with. Within our cognitive scope, this paper serves as a pioneering attempt for event‐based control of RDE systems. And the validity of the results is corroborated by two simulation examples.

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Adaptive tracking control for a class of random pure‐feedback nonlinear systems with Markovian switching

Cited by 26 publications

References 44 publications

Switched adaptive control for a class of switched nontriangular nonlinear systems with vanishing control gains

Switched adaptive control for a class of switched nontriangular nonlinear systems with vanishing control gains

Adaptive Synchronization for Uncertain Delayed Fractional-Order Hopfield Neural Networks via Fractional-Order Sliding Mode Control

Event‐triggered control for a class of nonlinear random systems involving time‐varying delay and exogenous disturbances

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