Distributed MPC based on robustly controllable sets for PWA systems

Abstract

The optimization problem in model predictive control (MPC) algorithm for piecewise affine (PWA) systems often contains substantial logic variables, which requires extensive computing power for online implementation. This paper proposes a one-step distributed MPC algorithm for spatially interconnected PWA systems with both input and state constraints, where the algorithm is based on a series of r-step robustly controllable sets. Algorithms for offline computing terminal sets and a series of r-step robustly controllable sets are developed using the step-by-step backward approach. The states that lie in the robustly controllable sets are steered into the terminal set in finite steps and ultimately converge into a robustly positively invariant set. The proposed algorithm is demonstrated to significantly reduce the online computational burden. Simulation results are provided to showcase the effectiveness of the algorithm.