Bang-bang control for uncertain random continuous-time switched systems

Yang Chang; Guangyang Liu; Hongyan Yan; Yang Chang; Guangyang Liu; Hongyan Yan

doi:10.3934/math.2025076

AIMS Mathematics

2025, Volume 10, Issue 1: 1645-1674. doi: 10.3934/math.2025076

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Research article

Bang-bang control for uncertain random continuous-time switched systems

School of Science, Nanjing Forestry University, Nanjing 210037, China

Received: 25 August 2024 Revised: 20 December 2024 Accepted: 25 December 2024 Published: 23 January 2025
MSC : 93C55, 49L20

In this paper, optimal control problems concerning uncertain random continuous-time switched system were studied. First, by applying Belleman's principle of optimality and chance theory, an optimality equation was derived. It's an extension of the equation of optimality from uncertain environment to uncertain random environment. Then, the optimality equation was employed to get bang-bang control for the control problems with the linear performances. Second, a two-stage algorithm was applied to implement optimal control. A genetic algorithm and Brent algorithm were used in the second stage in order to search the optimal switching instants in the numerical example. Finally, as an application of our theoretical results, an optimal cash holding problem was discussed and a corresponding optimal cash holding level was provided.
- uncertain random continuous-time switched system,
- chance theory,
- optimal control,
- cash holding problem
Citation: Yang Chang, Guangyang Liu, Hongyan Yan. Bang-bang control for uncertain random continuous-time switched systems[J]. AIMS Mathematics, 2025, 10(1): 1645-1674. doi: 10.3934/math.2025076

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Abstract

In this paper, optimal control problems concerning uncertain random continuous-time switched system were studied. First, by applying Belleman's principle of optimality and chance theory, an optimality equation was derived. It's an extension of the equation of optimality from uncertain environment to uncertain random environment. Then, the optimality equation was employed to get bang-bang control for the control problems with the linear performances. Second, a two-stage algorithm was applied to implement optimal control. A genetic algorithm and Brent algorithm were used in the second stage in order to search the optimal switching instants in the numerical example. Finally, as an application of our theoretical results, an optimal cash holding problem was discussed and a corresponding optimal cash holding level was provided.

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