Stabilization of switched nonlinear systems using predictive control

In this work, a predictive control framework is proposed for the constrained stabilization of switched nonlinear systems that transit between their constituent modes at prescribed switching times. The main idea is to design a Lyapunov-based predictive controller for each constituent mode in which the switched system operates, and incorporate constraints in the predictive controller design to ensure that the prescribed transitions between the modes occur in a way that guarantees stability of the switched closed-loop system. This is achieved as follows: for each constituent mode, a Lyapunov-based model predictive controller (MPC) is designed, and an analytic bounded controller, using the same Lyapunov function, is used to explicitly characterize a set of initial conditions for which the MPC, irrespective of the controller parameters, is guaranteed to be feasible, and hence stabilizing. Then, constraints are incorporated in the MPC design which, upon satisfaction, ensure that: (1) the state of the closed-loop system, at the time of the transition, resides in the stability region of the mode that the system is switched into, and (2) the Lyapunov function for each mode is non-increasing wherever the mode is re-activated, thereby guaranteeing stability.