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Optimal Control of Degrading Units through Threshold-Based Control Policies

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  • Dmitry Efrosinin

    (Institute of Stochastics, Johannes Kepler University Linz, 4040 Linz, Austria
    Department of Information Technologies, Faculty of Mathematics and Natural Sciences, Peoples’ Friendship University of Russia (RUDN University), 117198 Moscow, Russia)

  • Natalia Stepanova

    (Laboratory N17, Trapeznikov Institute of Control Sciences of RAS, 117997 Moscow, Russia)

Abstract

Optimal control problems are applied to a variety of dynamical systems with a random law of motion. In this paper we show that the random degradation processes defined on a discrete set of intermediate degradation states are also suitable for formulating and solving optimization problems and finding an appropriate optimal control policy. Two degradation models are considered in this paper: with random time to an instantaneous failure and with random time to a preventive maintenance. In both cases, a threshold-based control policy with two thresholds levels defining the signal state, after which an instantaneous failure or preventive maintenance can occur after a random time, and a maximum number of intermediate degradation states is applied. The optimal control problem is mainly solved in a steady-state regime. The main loss functional is formulated as the average cost per unit of time for a given cost structure. The Markov degradation models are used for numerical calculations of the optimal threshold policy and reliability function of the studied degrading units.

Suggested Citation

  • Dmitry Efrosinin & Natalia Stepanova, 2022. "Optimal Control of Degrading Units through Threshold-Based Control Policies," Mathematics, MDPI, vol. 10(21), pages 1-16, November.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:21:p:4098-:d:961776
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    References listed on IDEAS

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    1. Massimiliano Giorgio & Maurizio Guida & Gianpaolo Pulcini, 2011. "An age- and state-dependent Markov model for degradation processes," IISE Transactions, Taylor & Francis Journals, vol. 43(9), pages 621-632.
    2. Singpurwalla, Nozer D., 2006. "The Hazard Potential: Introduction and Overview," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1705-1717, December.
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