A Computationally Efficient Stabilizing Model Predictive Control of Switched Systems

Abstract

Many applications in engineering exhibit switching character due to discrete and continuous aspects in their dynamic behavior. Switching characteristics of hybrid systems bring discontinuity and nonlinearity in their course of operation and pose major challenges in developing stabilizing Model Predictive Control (MPC) for them. For Piecewise Affine (PWA) Systems, the MPC problem requires on-line solution of Mixed Integer Programs (MIPs) for obtaining the input profile. Since, complexity of the optimization problem that needs to be solved in MPC increases combinatorially with respect to the integer variables, on-line computing of MPC control law for large scale problems and/or problems with large horizons is expensive. In this paper we, propose a MPC formulation, under the popular framework of terminal cost - terminal set MPC, which enables tuning the complexity of the control algorithm. The proposed approach introduces an idea of a pre-terminal set, within which the inputs have enough power to trap states inside it. Since the pre-terminal set lies in the terminal mode which contains origin, this eliminates the need for binary decision variables to model mode transitions after the trajectory enters in pre-terminal set, thereby reducing the on-line complexity although at the expense of optimality. Examples are presented to illustrate the computational benefits of the proposed MPC strategy over existing MPC.