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Ergodic Control of Switching Diffusions
MARYLAND UNIV COLLEGE PARK INST FOR SYSTEMS RESEARCH
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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.
APPROVED FOR PUBLIC RELEASE