Indirect adaptive robust control of nonlinear systems with time‐varying parameters in a strict feedback form

控制理论(社会学) 反推 控制器(灌溉) 非线性系统 自适应控制 鲁棒控制 标识符 计算机科学 数学 上下界 控制(管理) 量子力学 生物 物理 数学分析 人工智能 程序设计语言 农学
作者
Jinbo Wu,Jiafeng Zhao,Donglai Wu
出处
期刊:International Journal of Robust and Nonlinear Control [Wiley]
卷期号:28 (13): 3835-3851 被引量:37
标识
DOI:10.1002/rnc.4107
摘要

Summary Without any prior knowledge of the physical bounds of unknown parameters and uncertain nonlinearities, an indirect adaptive robust controller is constructed for uncertain nonlinear time‐varying systems in a strict‐feedback form. Firstly, an adaptive strong robust controller is derived based on the command filtered adaptive backstepping approach. This controller not only can guarantee the boundedness of the closed‐loop system signals in the presence of time‐varying (TV) parameters and uncertain nonlinearities but also obviate the need to compute analytic derivatives of virtual control functions. Thus, the problem of “explosion of terms” in the standard adaptive backstepping technique is avoided. Through introduction of a simple adaptation law on the upper bound of uncertainties, a smooth robust control term is used to realize the disturbance attenuation. Afterwards, based on the nonlinear X‐swapping techniques, a modular approach in which the controller and the identifier can be designed separately is exploited. A novel algorithm is proposed to estimate the TV parameters accurately. By adopting the variation trend of the covariance matrix as an indicator of the driving signals' persistent excitation level, this online parameter estimation law is switched between a modified least‐squares algorithm and a gradient algorithm based on fixed σ ‐modification. Finally, a series of properties on the asymptotic stability and the global uniform ultimate boundedness of the closed‐loop system is established. Simulation results verify the effectiveness of the suggested method.

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