Temporal Lagrangian decomposition of model predictive control for hybrid systems

Given a model predictive control (MPC) problem for a hybrid system in the mixed logical dynamical (MLD) framework, a temporal decomposition scheme is proposed that efficiently derives the control actions by performing Lagrangian decomposition on the prediction horizon. The algorithm translates the original optimal control problem into a temporal sequence of independent subproblems of smaller dimension. The solution of the Lagrangian problem yields a sequence of control actions for the full horizon that is approximate in nature due to the non-convexity of the hybrid optimal control problem formulation and the consequent duality gap. For cases, however, where the duality gap is sufficiently narrow, the approximate control law will yield almost the same closed-loop behavior as the one obtained from the original optimal controller, but with a considerably smaller computational burden. An example, for which a reduction of the computation time by an order of magnitude is achieved, illustrates the algorithm and confirms its effectiveness.