Article ID: | iaor19981800 |
Volume: | 35 |
Issue: | 6 |
Start Page Number: | 1952 |
End Page Number: | 1988 |
Publication Date: | Nov 1997 |
Journal: | SIAM Journal on Control and Optimization |
Authors: | Ghosh Mrinal K., Marcus Steven I., Arapostathis Aristotle |
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 HJB equations. As an example we apply the results to a failure-prone manufacturing system and obtain closed form solutions for the optimal policy.