An efficient algorithm for optimal control of hybrid dynamical systems utilizing mode transition rule

Model predictive control based on the mixed logical dynamical (MLD) model is known as an effective approach to control of hybrid dynamical systems. This control problem can be formulated as a series of mixed integer quadratic (or linear) programming problems, though they are generally hard to compute exact solutions. Continuous relaxation and branch-and-bound method have been typically used to overcome this difficulty, but the current state is still far from satisfactory for real-time predictive control. It should be noticed that, in many physical hybrid control problem, "mode transition rule" is often given together with system model in advance; In this paper, we indicate a weak point of the existing method that it wastes the mode transition information due to continuous relaxation, and propose a modified algorithm which takes the information into consideration, so that it is completely utilized to narrow search space of branched subproblems. Numerical simulation will show that computational efficiency is well improved by the proposed method.