Model predictive control of switched affine systems with dwell time constraints—Efficient formulation, approximation and embedded implementation

Abstract

In this work, we study the problem of designing a model predictive control (MPC) strategy for switched affine systems with dwell time constraints. We show that the task of simultaneous determination of the optimal operational mode and actuator inputs can be formulated within the generalized disjunctive programming (GDP) framework and highlight its computational advantages over traditional techniques. Although GDP provides an efficient parametrization of the associated mixed integer program, the combinatorial nature of the problem might require a large computational time limiting its applicability in real time scenarios. To this end, we propose a framework based on the multitask learning paradigm to approximate the solution of mixed integer MPC for switched affine systems. We also provide a computational method based on the offline solution of a mixed integer linear program to overapproximate the reachable sets of the closed loop system that helps to analyze the safety and stability of the system under the influence of the learned controller. Once trained offline, the resulting controller results in a solver free approach well suited for implementation on a resource constrained embedded hardware. Several illustrative examples are provided to show the efficacy of the proposed approach.