Adaptive Nonsmooth State-Feedback Stabilization of Cascade Output-Constrained Uncertain Switched Systems

In this article, the problem of adaptive nonsmooth state-feedback stabilization for uncertain output-constrained cascade switched systems with a general form, whose subsystems possess mixed powers (MPs) and zero dynamics (ZDs), is investigated. To solve the problem of adaptive control, on subsystems of switched systems, some mild assumptions, such as ZDs with input-to-state stability (ISS), nonlinear terms with a growth condition and some well-known small signal conditions, have been imposed. State-feedback control laws are designed and an adaptive law is constructed in a systematic way by revamping the so-called adding a power integrator (AAPI) technique, a special back-stepping-like method. In order to cope with output constraints (OCs), a common Lyapunov function, including a tangent-type barrier Lyapunov function term, is constructed. The method is proposed in a unified manner which can tackle adaptive stabilization of switched systems due to that it can deal with the cases of uncertain cascade switched systems with/without OCs, no need to change the structure of the controller. Simulation results are provided to illustrate the efficiency of the proposed method.