Adaptive finite time controller design for switched systems with unknown parameters, mismatched uncertain terms, external disturbances and input perturbations.

Abstract

The main objective of this study concerns with the problem of control and stabilization design schemes for a class of nonlinear switching systems whose dynamics are excited with an undetermined switching logic. Several conditions are taken into account for the subsystems of the whole structure to mimic the natural properties of the real-world nonlinear physical systems. The first is to assume that there is no prior information about the values of the system parameters. The second is to add matched and mismatched uncertain terms to the system dynamics. Furthermore, the effects of the input fluctuations in the actuator model are reflected via gain variations. We assume that the dynamic of a part of the system is uncertain and fully unknown with no control inputs to be relaxed as mismatching uncertainties. And, it is supposed that there is no previous knowledge about the bounds of the lumped uncertainties. To cope the mentioned issues, a robust adaptive control methodology is proposed in this paper. One of the main attributes of the designed control approach is that it guarantees the fast convergence of the system responses to zero with a (practical) finite settling time. A Lyapunov function tactic is then constructed to confirm the theoretic findings of the study. It is also demonstrated that the same controller is applicable for the switched systems perturbed by unknown input saturation nonlinearities. As a result, the chief contributions of this article involve: (1) handling the effects of the system unknown dynamics, external perturbations, unmatched uncertainties, control input variations, unknown parameters and input saturation limiter with no prior information about them and (2) providing a simple effective adaptive algorithm which ensures the fast finite time stability of the entire system under any arbitrary switch schemes. The provided computer simulations highlight the effective performance of the introduced adaptive control technology.