Stabilization of a class of cascade nonlinear switched systems with application to chaotic systems

In this study, the problem of finite-time practical control of a class of nonlinear switched systems in the presence of input nonlinearities is investigated. The subsystems of the switched system are considered as complex nonlinear systems with a cascade structure. Each subsystem is fluctuated by lumped uncertainties. Moreover, some parts of the system's dynamics are considered to be unknown in advance. This paper sets no restrictive assumption on the switching logic of the system. Therefore, the aim is to propose a controller to work under any arbitrary switching signals. After providing a smooth sliding manifold, a simple adaptive control input is developed such that the system trajectories approach the prescribed sliding mode dynamics in finite-time sense. The adopted control signal does not use the upper bounds of the lumped uncertainties, and it is robust against unknown nonlinear parts of the subsystems. It is proved that the origin is the (practical) finite-time stable equilibrium point of the overall closed-loop system. Subsequently, the proposed control rule is modified to handle the same switched system with no input nonlinearities. Computer simulations via 2 chaotic electric direct current machines demonstrate the robust performance of the derived variable structure control algorithm against system fluctuations and nonlinear inputs.