A new model reference adaptive control structure for uncertain switched systems with unmodeled input dynamics

Abstract

In this paper, a new model reference adaptive controller (MRAC) for uncertain switched linear systems is developed. A class of uncertain switched linear systems with parametric mismatched and input matched uncertainties, control input effectiveness and unmodeled dynamics is studied in this paper. The difference in input matrix for different switching modes which means the input channel degradation is investigated through this paper. By using common Lyapunov function method and developing new linear matrix inequality based sufficient conditions, uniform ultimate boundedness of the reference tracking error is guaranteed by switched MRAC and by using a novel nonlinear controller term, the size of the uniform ultimate bounded region can be made arbitrarily small which could enhance the performance of the overall control structure. Modified versions of MRAC systems using low-frequency learning adaptation MRAC is also used for better transient performance at switching instants. An illustrative numerical example demonstrates the performance of the proposed approach. Results also show that for the cases without parametric uncertainty in the linear part, asymptotic stability of the reference tracking error is guaranteed.