Optimal Guaranteed Cost Sliding Mode Control for Constrained-Input Nonlinear Systems With Matched and Unmatched Disturbances

Zhang, Huaguang; Qu, Qiuxia; Xiao, Geyang; Cui, Yang

doi:10.1109/tnnls.2018.2791419

Cited by 85 publications

(56 citation statements)

References 47 publications

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“…To address the issue, this paper uses the trial-and-error method to obtain the initial admissible control policies, which is in the same spirit as the work of Yang et al 38 2. It seems to be challengeable to solve (30) for V ( j) (x), u ( j + 1) (x), and ( j + 1) (x). Fortunately, by using actor and critic approximators as well as the method of weighted residuals, 39 we can derive V ( j) (x), u ( j + 1) (x), and ( j + 1) (x) via (30).…”

Section: Off-policy Iteration Algorithmmentioning

confidence: 99%

“…It seems to be challengeable to solve (30) for V ( j) (x), u ( j + 1) (x), and ( j + 1) (x). Fortunately, by using actor and critic approximators as well as the method of weighted residuals, 39 we can derive V ( j) (x), u ( j + 1) (x), and ( j + 1) (x) via (30). The detailed procedure is illustrated in Section 4.2.…”

Section: Off-policy Iteration Algorithmmentioning

confidence: 99%

“… The off‐policy iteration algorithm combined with an indirect method is used to solve the constrained robust stabilization problem for the first time. In comparison with the existing literature, the control algorithm proposed in this paper no longer requires a priori knowledge of internal dynamics (that is, f ( x ) in subsequent system ). More importantly, the present control algorithm can relax the PE condition (see Remark ). Unlike the related works, obtaining robust controllers via solving H ∞ optimal control problems, this paper derives the robust controllers by solving H 2 optimal control problems.…”

Section: Introductionmentioning

confidence: 99%

“…26,27 Over the past several years, RL and ADP have been widely used to solve robust nonlinear control problems. [28][29][30] Modares et al 28 introduced an RL-based online learning algorithm to solve the H ∞ control problem of continuous-time (CT) constrained systems. To implement the online learning algorithm, the AC structure was employed.…”

Section: Introductionmentioning

confidence: 99%

“…Assume that u (0) (x) ∈ (Ω) and (0) (x) ∈ (Ω). If the sequence pair{ V ( ) (x), u ( ) (x), ( ) (x) }is determined by(30), then, for all x ∈ Ω, we havelim →∞ V ( ) (x) = V * (x),lim →∞ u ( ) (x) = u * (x), and lim →∞ ( ) (x) = * (x).…”

mentioning

confidence: 99%

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An off‐policy iteration algorithm for robust stabilization of constrained‐input uncertain nonlinear systems

Yang

Wei

2018

Intl J Robust & Nonlinear

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Summary This paper studies the robust stabilization problem of constrained‐input nonlinear systems with mismatched uncertainties. Initially, the robust stabilization problem is converted into a constrained H2 optimal control problem by providing a proper infinite‐horizon cost function for the auxiliary system. It is demonstrated that the solution of the constrained H2 optimal control problem can force the original system to be stable in the sense of uniform ultimate boundedness. Then, under the framework of reinforcement learning, an off‐policy iteration algorithm is proposed to solve the constrained H2 optimal control problem. The off‐policy iteration algorithm is implemented by using two kinds of approximators. That is, the critic approximator is applied to approximate the optimal cost function and the actor approximator is used to approximate the augmented optimal control. The method of weighted residuals together with the Monte‐Carlo integration technique is employed to determine the weight parameters of critic and actor approximators. Finally, two examples, including a pendulum system, are presented to validate the proposed control algorithm.

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Section: Off-policy Iteration Algorithmmentioning

confidence: 99%

Section: Off-policy Iteration Algorithmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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An off‐policy iteration algorithm for robust stabilization of constrained‐input uncertain nonlinear systems

Yang

Wei

2018

Intl J Robust & Nonlinear

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Observer‐based single‐network incremental adaptive dynamic programming for fault‐tolerant control of nonlinear systems with actuator faults

Zhang

2022

Adaptive Control & Signal

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Summary A model‐free incremental adaptive fault‐tolerant control (FTC) scheme is proposed for a class of nonlinear systems with actuator faults. To deal with actuator faults and guarantee the approximate optimal performance of the nominal nonlinear system without any prior knowledge of system dynamics, a single‐network incremental adaptive dynamic programming (SIADP) algorithm based on incremental neural network observer is developed to design an active fault‐tolerant control (AFTC) policy. An approximate linear time‐varying system is obtained by incremental nonlinear technique, in which the relevant matrix parameters are identified by recursive least square estimation. Then, a SIADP algorithm‐based fault‐tolerant controller is developed. Based on the redundancy characteristic and function of actuators, a grouping scheme of actuators is introduced. An incremental neural network observer is designed to approximate the actuator faults. The novel SIADP scheme is constructed with a simplified single critic neural network to shorten the learning time and decrease the computational burden in the control process, in which the norm of the weight estimations of critic neural network is updated. Moreover, based on the Lyapunov theorem, the uniformly ultimately bounded stability of the closed‐loop incremental system is proved. Finally, simulations are given to verify the effectiveness of the proposed FTC scheme.

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Partial model‐free sliding mode control design for a class of disturbed systems via computational learning algorithm

Zhou

Huang

Song

et al. 2021

Optim Control Appl Methods

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In this article, a partial model‐free sliding mode control (SMC) strategy is proposed for a class of disturbed systems. A partial model‐free SMC law is designed to attenuate the matched external disturbances by just employing partial dynamics information. A complete model‐free policy iteration algorithm is integrated to the designed SMC scheme such that the optimal control performance of the disturbed system is achieved. The implementation of the proposed partial model‐free SMC strategy is based on a computational learning algorithm, which involves date collection, policy iteration, and optimal control phases. The feasibility of the proposed SMC strategy in data collection phase and optimal control phase are analyzed, respectively. Finally, a numerical example is employed to verify the effectiveness of the proposed SMC strategy.

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Optimal Guaranteed Cost Sliding Mode Control for Constrained-Input Nonlinear Systems With Matched and Unmatched Disturbances

Cited by 85 publications

References 47 publications

An off‐policy iteration algorithm for robust stabilization of constrained‐input uncertain nonlinear systems

An off‐policy iteration algorithm for robust stabilization of constrained‐input uncertain nonlinear systems

Observer‐based single‐network incremental adaptive dynamic programming for fault‐tolerant control of nonlinear systems with actuator faults

Partial model‐free sliding mode control design for a class of disturbed systems via computational learning algorithm

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