Ergodic Control of Switching Diffusions

Authors:
Mrinal K. Ghosh;Aristotle Arapostathis;Steven I. Marcus
Affiliations:
-;-;-
Venue:
SIAM Journal on Control and Optimization
Year:
1997

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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 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.