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Model predictive control problems for constrained hybrid systems are usuallycast as mixed-integer optimization problems (MIP). However, commercial MIPsolvers are designed to run on desktop computing platforms and are not suitedfor embedded applications which are typically restricted by limitedcomputational power and memory. To alleviate these restrictions, we develop anovel low-complexity, iterative method for a class of non-convex, non-smoothoptimization problems. This class of problems encompasses hybrid modelpredictive control problems where the dynamics are piece-wise affine (PWA). Wegive conditions such that the proposed algorithm has fixed points and showthat, under practical assumptions, our method is guaranteed to converge locallyto local minima. This is in contrast to other low-complexity methods in theliterature, such as the non-convex alternating directions method of multipliers(ADMM), for which no such guarantees are known for this class of problems. Byinterpreting the PWA dynamics as a union of polyhedra we can exploit theproblem structure and develop an algorithm based on operator splittingprocedures. Our algorithm departs from the traditional MIP formulation, andleads to a simple, embeddable method that only requires matrix-vectormultiplications and small-scale projections onto polyhedra. We illustrate theefficacy of the method on two numerical examples, achieving good closed-loopperformance with computational times several orders of magnitude smallercompared to state-of-the-art MIP solvers. Moreover, it is competitive with ADMMin terms of suboptimality and computation time, but additionally provides localoptimality and local convergence guarantees.

Low-complexity method for hybrid MPC with local guarantees