A logic-based hybrid solver for optimal control of hybrid systems

Combinatorial optimization over continuous and integer variables was proposed recently as an useful tool for solving complex optimal control problems for linear hybrid dynamical systems formulated in discrete-time. Current approaches are based on mixed-integer linear/quadratic programming (MIP), which provides the solution after solving a sequence of relaxed standard linear (or quadratic) programs (LP, QP). An MIP formulation has the drawback of requiring that the discrete/logic part of the hybrid problem needs to be converted to into mixed-integer inequalities. Although this operation can be done automatically, most of the original discrete structure of the problem is lost during the conversion. Moreover, the efficiency of the MIP solver only relies upon the tightness of the continuous LP/QP relaxations. In this paper we attempt at overcoming such difficulties by combining MIP and constraint programming (CP) techniques into a "hybrid" solver, taking advantage of CP for dealing efficiently with satisfiability of logic constraints. We detail how to model the hybrid dynamics so that the optimal control problem can be solved by the hybrid MIP+CP solver, and show on a case study that the achieved performance is superior to the one achieved by pure MIP solvers.