A semidefinite programming approach for stochastic switched optimal control problems

We consider solving stochastic switched optimal control problems (SSOCPs) with polynomial data using sum-of-squares (S.O.S) and semidefinite programming (SDP), where both the number of switches and the switching signal are not known in advance. The problem is transformed into an embedded form using a new control variable that is responsible for controlling the switching policy. Then, through a hierarchy of polynomial S.O.S problems, we find an approximation of the value function corresponding to the original optimal control problem and use it to design feedback control. Finally, one simulation experiment is included to demonstrate the performance of our new approach.