OPTIMAL CONTROL IN HYBRID SYSTEMS: AN EFFICIENT DECISION MAKING TOOL

Abstract. Hybrid systems evolve simultaneously in continuous and discrete state spaces. An illustration of practical interest is realized by continuous systems for which decisions have to be made at discrete times. We set this problem as an optimal control problem, whereby the decisions become controls that are implemented in order to optimize a certain desired outcome. Due to the intertwining between continuous and discrete dynamics, the derivation of the adjoint and optimality systems is different from the purely continuous or discrete cases. We obtain the necessary optimality conditions and, for a few typical illustrations, we obtain also explicit expressions for the optimal controls