Ergodic Control of Switching Diffusions

Abstract

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