Separation theorem for average optimal control for hybrid systems of variable dimension

We consider the problem of average optimal control for a linear hybrid system whose continuous motion alternates with discrete changes (switchings) that change the state space. The initial system state is random. The control quality is characterized by the mean value of a quadratic functional. Switching times and their number are not known in advance. They are determined by minimizing the functional. For the problem under consideration, the classical separation principle does not hold. We prove the so-called conditional separation principle. We also show sample applications of conditional and classical separation principles.