Optimal control of a hybrid system with pathwise average cost

The authors study the ergodic control problem of switching diffusions of representing a typical hybrid system that arises in numerous applications such as fault-tolerant control systems and flexible manufacturing systems. Under certain conditions, they establish the existence of a stable Markov nonrandomized policy which is almost certainly optimal for the pathwise long-run average cost criterion. They they study the corresponding Hamilton-Jacobi-Bellman (HJB) equation and establish the existence of a unique solution in a certain class. Using this, they characterize the optimal policy as a minimizing selector of the Hamiltonian associated with the HJB equations. They apply these results to a failure-prone manufacturing system and show that the optimal production rate is of the hedging point type