A Generalization of a Polynomial Optimal Control of Switched Systems

A generalization of a polynomial approach to solve the optimal control problem of nonlinear switched systems is presented. We present a technique to deal with the more general non-polynomial switched systems, using the polynomial approach previously presented, combined with a recasting process. It is shown that the representation of the original switched problem into a continuous polynomial system allows us to use the generalized Maximum Principle. With this method and from a theoretical point of view, we provide necessary and sufficient conditions for the existence of minimizer by using particular features of its relaxed, convex formulation using the theory of moments.