Optimal Control of Degrading Units through Threshold-Based Control Policies

Dmitry Efrosinin () and Natalia Stepanova
Additional contact information
Dmitry Efrosinin: Institute of Stochastics, Johannes Kepler University Linz, 4040 Linz, Austria
Natalia Stepanova: Laboratory N17, Trapeznikov Institute of Control Sciences of RAS, 117997 Moscow, Russia

Mathematics, 2022, vol. 10, issue 21, 1-16

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.

Keywords: degradation process; optimal control problem; threshold-based policy; average cost; Markov death process; reliability function (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/10/21/4098/pdf (application/pdf)
https://www.mdpi.com/2227-7390/10/21/4098/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:10:y:2022:i:21:p:4098-:d:961776

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().