Warm Start of Mixed-Integer Programs for Model Predictive Control of Hybrid Systems

In hybrid model predictive control (MPC), a mixed-integer quadratic program (MIQP) is solved at each sampling time to compute the optimal control action. Although these optimizations are generally very demanding, in MPC, we expect consecutive problem instances to be nearly identical. This article addresses the question of how computations performed at one time step can be reused to accelerate (warm start) the solution of subsequent MIQPs. Reoptimization is not a rare practice in integer programming: for small variations of certain problem data, the branch-and-bound algorithm allows an efficient reuse of its search tree and the dual bounds of its leaf nodes. In this article, we extend these ideas to the receding-horizon settings of MPC. The warm-start algorithm we propose copes naturally with arbitrary model errors, has a negligible computational cost, and frequently enables an a priori pruning of most of the search space. Theoretical considerations and experimental evidence show that the proposed method tends to reduce the combinatorial complexity of the hybrid MPC problem to that of a one-step look-ahead optimization, greatly easing the online computation burden.