A framework for stability analysis of high-order nonlinear systems based on the CMAC method

A framework for analyzing the stability of a class of high-order minimum-phase nonlinear systems of relative degree two based on the characteristic model-based adaptive control (CMAC) method is presented. In particular, concerning the tracking problem for such high-order nonlinear systems, by introducing a consistency condition for quantitatively describing modeling errors corresponding to a group of characteristic models together with a certain kind of CMAC laws, we prove closed-loop stability and show that such controllers can make output tracking error arbitrarily small. Furthermore, following this framework, with a specific characteristic model and a golden-section adaptive controller, detailed sufficient conditions to stabilize such groups of highorder nonlinear systems are presented and, at the same time, tracking performance is analyzed. Our results provide a new perspective for exploring the stability of some high-order nonlinear plants under CMAC, and lay certain theoretical foundations for practical applications of the CMAC method.抽象创新点本文建立了基于特征模型的采样控制方法与一类高阶对象组成闭环系统的稳定性分析框架. 具体针对一类相对阶为二的 最小相位非线性不确定系统的位置跟踪问题, 通过引入刻画特征模型容许建模误差的相容性条件, 证明了一类基于特征 模型的采样控制器与原系统组成闭环系统的稳定性, 并且输出跟踪误差能够保证足够小. 进一步根据所建立的稳定性分 析框架, 针对上述位置跟踪问题, 给出了对应的特征模型, 黄金分割自适应控制, 以及具体的闭环稳定条件. 本文的研 究结果为基于特征模型自适应控制方法的闭环稳定性分析提供了新的研究思路, 为该方法的工程应用奠定了理论基础.

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