Optimal Repair Policies for Systems Deteriorating After Disruptions

We consider a scenario where a system experiences a disruption, and the states (representing health values) of its components continue to reduce over time, unless they are acted upon by a controller. Given this dynamical setting, we consider the problem of finding an optimal control (or switching) s...

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Bibliographic Details
Published in:IEEE transactions on automatic control 2022-07, Vol.67 (7), p.3426-3441
Main Authors: Gehlot, Hemant, Sundaram, Shreyas, Ukkusuri, Satish
Format: Article
Language:English
Subjects:
cyber-physical systems
Deterioration
Indexes
Maintenance engineering
Optimal control
optimization
Repair
resilience
Servers
Switched systems
Switches
Task analysis
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Summary:We consider a scenario where a system experiences a disruption, and the states (representing health values) of its components continue to reduce over time, unless they are acted upon by a controller. Given this dynamical setting, we consider the problem of finding an optimal control (or switching) sequence to maximize the sum of the weights of the components, whose states are brought back to the maximum value. We first provide several characteristics of the optimal policy for the general (fully heterogeneous) version of this problem. We then show that under certain conditions on the rates of repair and deterioration, we can explicitly characterize the optimal control policy as a function of the states. When the deterioration rate (when not being repaired) is larger than or equal to the repair rate, and the deterioration and repair rates as well as the weights are homogeneous across all the components, we show that the policy that targets the component with the largest state value at each time step is optimal under certain conditions. On the other hand, if the repair rates are sufficiently larger than the deterioration rates, the optimal control policy is to target the component whose state minus the deterioration rate is least in a particular subset of components at each time step.
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2021.3103902