SIAM Journal on Control and Optimization, Vol.35, No.6, 1952-1988, 1997
Ergodic Control of Switching Diffusions
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 fairly general conditions, we Establish the existence of a stable, nonrandomized Markov policy which almost surely minimizes the pathwise 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 policy as a minimizing selector of the Hamiltonian associated with the HJB equations. As an example we apply the results to a failure-prone manufacturing system and obtain closed form solutions for the optimal policy.