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Modified Model Free Adaptive Control for a Class of Nonlinear Systems with Multi-threshold Quantized Observations

Xiangquan Li, Zhengguang Xu*, Yanrong Lu, Jiarui Cui, and Lixin Zhang
International Journal of Control, Automation, and Systems, vol. 19, no. 10, pp.3285-3296, 2021

Abstract : This paper addresses a pattern-moving-based modified model free adaptive control (PMFAC) scheme and illustrates the convergence of its tracking error for a class of nonlinear systems with unknown model and multi-threshold quantized observations. The basic idea is to consider the system’s quantization error as an external disturbance and an improved performance index function of control law is proposed from the perspective of twoplayer zero-sum game (TP-ZSG) based on the existed MFAC algorithms. The PMFAC scheme is established which mainly includes an improved tracking control law and a pseudo-partial derivative (PPD) estimation algorithm. Under certain conditions, the bounded convergence of system tracking error and the stability of PMFAC system with quantization errors can be guaranteed. The theoretical results are demonstrated by two numerical examples.

Keyword : Adaptive tracking control, model free adaptive control (MFAC), multi-threshold quantized observations, pattern moving, two-player zero-sum game.

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