Ergodic control of switching diffusions

Ghosh, Mrinal K. ; Arapostathis, Aristotle ; Marcus, Steven I. (1997) Ergodic control of switching diffusions SIAM Journal on Control and Optimization, 35 (6). pp. 1952-1988. ISSN 0363-0129

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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.

Item Type:Article
Source:Copyright of this article belongs to Society for Industrial and Applied Mathematics.
Keywords:Switching Diffusions; Markov Policy; Ergodicity; Pathwise Average Cost; Hamilton-jacobi-bellman Equations
ID Code:72602
Deposited On:09 Jan 2012 09:46
Last Modified:09 Jan 2012 09:46

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