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 paper 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 paper 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