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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 expectconsecutive problem instances to be nearly identical. This paper addresses thequestion of how computations performed at one time step can be reused toaccelerate (warm start) the solution of subsequent MIQPs.  Reoptimization is not a rare practice in integer programming: for smallvariations of certain problem data, the branch-and-bound algorithm allows anefficient reuse of its search tree and the dual bounds of its leaf nodes. Inthis paper we extend these ideas to the receding-horizon settings of MPC. Thewarm-start algorithm we propose copes naturally with arbitrary model errors,has a negligible computational cost, and frequently enables an a-priori pruningof most of the search space. Theoretical considerations and experimentalevidence show that the proposed method tends to reduce the combinatorialcomplexity of the hybrid MPC problem to that of a one-step look-aheadoptimization, greatly easing the online computation burden.

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