A new method for control of nonlinear state-dependent switched systems

Abstract

In this paper, a new method for the control of input-affine nonlinear switched systems is introduced. The system switching conditions are assumed to be state-dependent, rather than the simpler input-dependent case. The main contribution of this research is that the effects of switched dynamics are interpreted as a model uncertainty bounded within a polynomial of states norms, with unknown coefficients. In order to prevent extra conservativeness, coefficients are tuned adaptively, so that a minimal state-varying bound could be achieved. This is unlike the conventional sliding mode control (SMC) scheme, where the existence of a constant and usually large upper bound must be presumed. To address the challenge of coping with such a new concept of uncertainty, an extended form of the original adaptive fuzzy sliding mode control scheme is proposed. Adaptation laws are used to tune a fuzzy controller and also real-time estimation of the instantaneous bound of uncertainties. Closed-loop stability is guaranteed by proposing a group of multiple Lyapunov functions (MLF) with tunable parameters. Except for the mild condition that the largest difference between the magnitudes of the sub-manifolds of the switched system is bounded by a polynomial of states with uncertain coefficients, the proposed method has the distinct advantage that no information about the dynamic equations or switching conditions is required in the control design stage. The proposed method is applied to the two challenging case studies, depicting the outstanding effectiveness of the method.