Robust Control of Partially Observable Failing Systems

This paper is concerned with optimal maintenance decision making in the presence of model misspecification. Specifically, we are interested in the situation where the decision maker fears that a nominal Bayesian model may be miss-specified or unrealistic, and would like to find policies that work well even when the underlying model is flawed. To this end, we formulate a robust dynamic optimization model for condition-based maintenance in which the decision maker explicitly accounts for distrust in the nominal Bayesian model by solving a worst-case problem against a second agent, “nature,” who has the ability to alter the underlying model distributions in an adversarial manner. The primary focus of our analysis is on establishing structural properties and insights that hold in the face of model miss-specification. In particular, we prove (i) an explicit characterization of nature’s optimal response through an analysis of the robust dynamic programming equation, (ii) convexity results for both the robust value function and the optimal robust stopping region, (iii) a general robustness result for the preventive maintenance paradigm, and (iv) the optimality of a robust control limit policy for the important subclass of Bayesian change point detection problems. We illustrate our theoretical result on a real-world application from the mining industry.