ERGODIC CONTROL OF SWITCHING DIFFUSIONS

We study the ergodic control problem of switching diffusions represent ing a typical hybrid system that arises in numerous applications such as fault-tolerant control systems, flexible manufacturing systems, etc . Under fairly general conditions, we Establish the existence of a sta ble, nonrandomized Markov policy which almost surely minimizes the pat hwise long-run average cost. 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 p olicy as a minimizing selector of the Hamiltonian associated with the HJB equations. As an example we apply the results to a failure-prone m anufacturing system and obtain closed form solutions for the optimal p olicy.