Abstract
ABSTRACTIn this paper, adaptive tracking control of switched nonlinear systems in the parametric strict-feedback form is investigated. After defining a reparametrisation lemma in the presence of a non-zero reference signal, we propose a new adaptive backstepping design of the virtual controllers that can handle the extra terms arising from the reparametrisation (and that the state-of-the-art backstepping designs cannot dominate). The proposed adaptive design guarantees, under arbitrarily fast switching, an a priori bound for the steady-state performance of the tracking error and a tunable bound for the transient error. Finally, the proposed method, by overcoming the need for subsystems with common sign of the input vector field, enlarges the class of uncertain switched nonlinear systems for which the adaptive tracking problem can be solved. A numerical example is provided to illustrate the proposed control scheme.
Highlights
Uncertainties and nonlinearities are ubiquitous when controlling complex systems
Some research has been conducted on adaptive control of switched nonlinear systems, which can be grouped into two families: (1) the nonlinear functions of the subsystems are unknown; (2) the nonlinear functions are parametrised with unknown constants
The problem to be solved in this work is formulated in the following: 2. Problem formulation and preliminaries This paper focuses on uncertain single-input-single-output switched nonlinear systems in the parametric strict-feedback form: Problem 2.1: Design a control input u and a group of adaptive laws such that the output of the uncertain switched nonlinear system (1) can track the reference signal ym with performance guarantee under arbitrarily fast switching
Summary
Uncertainties and nonlinearities are ubiquitous when controlling complex systems. As an effective method to cope with uncertainties and nonlinearities, adaptive control of nonlinear systems via backstepping approaches has been intensively studied in the last decades (Bechlioulis & Rovithakis, 2008; Chen & Tao, 2016; Ge, Hong, & Lee, 2005; Kojic & Annaswamy, 2005; Krstic, Kanellakopoulos, & Kokotovic, 1995; Mao, Huang, & Xiang, 2017; Yu, Fei, & Li, 2010; Yu, Zhang, & Fei, 2013; Zhou, Wen, & Li, 2012). KEYWORDS Adaptive tracking control; switched nonlinear systems; global ultimate boundedness; arbitrarily fast switching A big open problem remains concerning how to design, under arbitrarily fast switching, an adaptive tracking controller with prescribed performance guarantees for uncertain switched nonlinear systems whose subsystems have possibly different signs of the input vector field.
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