A decoupled adaptive control algorithm for global state feedback stabilization of a class of nonlinear systems

Summary The global stabilization problem for a class of stochastic time‐delay nonlinear systems with stochastic‐input‐to‐state‐stable–like conditions is investigated. Different from the existing results, the nonlinear growing conditions are more general, and the existences of the state and input time delays make the work more challenging in the control design and stability analysis. By introducing an appropriate gain‐scaling method and using a homogeneous domain control strategy, a delay‐independent controller is constructed to ensure that the equilibrium at the origin of the closed‐loop system is globally asymptotically stable in probability. Examples are given to show the validness of the proposed method.

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“…Lemma (See the work of Liu and Wu) Assume m and n are 2 positive real numbers and a ( x , y ) is a function. Then, for any

x, y \in double-struckR, c false(x, y false) > 0

, we have

false| a false(x, y false) x^{m} y^{n} false| \leq c false(x, y false) {false| x false|}^{m + n} + \frac{n}{m + n} {((), \frac{m}{false(m + n false) c false(x, y false)})}^{\frac{m}{n}} {false| a false(x, y false) false|}^{\frac{m + n}{n}} {false| y false|}^{m + n} .

…”

Section: Preliminary Resultsmentioning

confidence: 99%

Global stabilization for a class of stochastic nonlinear systems with SISS‐like conditions and time delay

Zhang

Xue

Jiang

2018

Intl J Robust & Nonlinear

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“…are constants, l 1 > 0 is the adaption gain, z i is defined by (6) and (8),Θ is the estimation of the unknown parameter Θ = Proof. By using (25) and Proposition 2, it follows that the derivative of…”

Section: Theorem 2 For Nonlinear System (1) Under Assumption 1 Thermentioning

confidence: 99%

New results on explicit adaptive control design for nonlinear systems with polynomial conditions

Liu

Xue

Sun

2020

Intl J Robust & Nonlinear

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This paper discusses the adaptive control problem for a class of nonlinear systems with polynomial growing conditions. By introducing a Lyapunov function which carries the quadratic terms and higher-order terms of the transformed variables and constructing an appropriate dynamic gain, a new control strategy is presented to design an adaptive controller using only one parameter estimation. Compared with the existing results, the presented method avoids the over-parameterization and significantly simplifies the control design. A modified version of the method which adopts no parameter estimation is also provided. It shows that all the signals of the closed-loop system are bounded and the solution of the original system converges to zero. A simulation example is given to show the validness of the method.

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“…Remark 1. It is worth mentioning that, if system (1) does not contain the stochastic term i, (t) (x)d , then it will become the nonlinear system discussed in the work of Mou et al 42 Furthermore, it should be noted that the adaptive control approaches in the aforementioned work 42 require that all the states are available for measurement.…”

Section: System Description and Basic Assumptionsmentioning

confidence: 99%

Adaptive fuzzy output‐feedback tracking control for switched stochastic pure‐feedback nonlinear systems

Chang

Wang

Alsaadi

et al. 2019

Adaptive Control & Signal

122

101

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This paper considers the problem of adaptive fuzzy output-feedback tracking control for a class of switched stochastic nonlinear systems in pure-feedback form. Unknown nonlinear functions and unmeasurable states are taken into account. Fuzzy logic systems are used to approximate the unknown nonlinear functions, and a fuzzy observer is designed to estimate the immeasurable states.Based on these methods, an adaptive fuzzy output-feedback control scheme is developed by combining the backstepping recursive design technique and the common Lyapunov function approach. It is shown that all the signals in the closed-loop system are semiglobally uniformly ultimately bounded in mean square in the sense of probability, and the observer errors and tracking errors can be regulated to a small neighborhood of the origin by choosing appropriate parameters. Finally, a simulation result is provided to show the effectiveness of the proposed control method. KEYWORDS adaptive fuzzy control, backstepping, pure-feedback form, state observer, switched stochastic systems Int J Adapt Control Signal Process. 2019;33:1567-1582.wileyonlinelibrary.com/journal/acs

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A decoupled adaptive control algorithm for global state feedback stabilization of a class of nonlinear systems

Cited by 19 publications

References 25 publications

Global stabilization for a class of stochastic nonlinear systems with SISS‐like conditions and time delay

Global stabilization for a class of stochastic nonlinear systems with SISS‐like conditions and time delay

New results on explicit adaptive control design for nonlinear systems with polynomial conditions

Adaptive fuzzy output‐feedback tracking control for switched stochastic pure‐feedback nonlinear systems

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