Embedded optimization for mixed logical dynamical systems

•First branch-and-bound hybrid MPC solver that targets embedded systems.•Problem-specific ANSI-C implementation can be automatically generated.•Efficient, problem-specific subtree cuts are generated by pre-processing methods.•Relaxations provide trade-off between performance and runtime.•Two extensive numerical studies demonstrating the effectiveness of the approach. Predictive control of hybrid systems is currently considered prohibitive using embedded computing platforms. To overcome this limitation for mixed logical dynamical systems of small to medium size, we propose to use (1) a standard branch-and-bound approach combined with a fast embedded interior point solver, (2) pre-processing heuristics, run once and offline, to significantly reduce the number of subproblems to be solved, and (3) relaxations of the original MPC problem that allow a trade off between computation time and closed-loop performance. A problem-specific ANSI C implementation of the proposed method can be automatically generated, and has a fixed memory footprint and a code size that is insignificantly larger than that of the subproblem solver. Two extensive numerical studies are presented, where problems with up to 60 binary variables are solved in less than 0.2s with a performance deterioration of below 2% when compared to an optimal MPC scheme.