A numerical framework for optimal control of switched affine systems with state constraint

In this paper, we address the problem of numerical implementation of optimal control for switched affine systems with state constraints. In order to properly solve the problem, a relaxed system is introduced and the connection between the solution of this system and the solution of the initial one is established. One of the main difficulties is then related to the fact that the optimal solution is generally singular. We show that, using slack variables, a set of complementarity constraints can be used to take into account the singular nature of the solution. The optimal control problem is then reformulated as a constraint optimization problem over the Hamiltonian systems and solved via a direct method. This formulation does not require a priori knowledge on the structure (regular/singular) of the solution. In addition, state path constraints are included. Numerical simulations for power converters, both in continuous and discontinuous conduction mode, illustrate the effectiveness of the proposed methodology.