Uncertain random problem for multistage switched systems

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

doi:10.3934/math.20231161

AIMS Mathematics

2023, Volume 8, Issue 10: 22789-22807. doi: 10.3934/math.20231161

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Research article Special Issues

Uncertain random problem for multistage switched systems

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

Received: 21 March 2023 Revised: 18 June 2023 Accepted: 25 June 2023 Published: 18 July 2023
MSC : 93C55, 49L20

Optimal control problems for switched systems how best to switch between different subsystems. In this paper, two kinds of linear quadratic optimal control problems for multistage switched systems composing of both randomness and uncertainty are studied. Chance theory brings us a useful tool to deal with this indeterminacy. Based on chance theory and Bellman's principle, the analytical expressions are derived for calculating both the optimal control input and the optimal switching control law. Optimal control is implemented by genetic algorithm instead of enumerating all the elements of a series of sets whose size grows exponentially. Finally, the results of numerical examples are provided to illustrate the effectiveness of the proposed method.
- chance theory,
- uncertain random multistage switched systems,
- optimal control,
- genetic algorithm
Citation: Guangyang Liu, Yang Chang, Hongyan Yan. Uncertain random problem for multistage switched systems[J]. AIMS Mathematics, 2023, 8(10): 22789-22807. doi: 10.3934/math.20231161

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Abstract

Optimal control problems for switched systems how best to switch between different subsystems. In this paper, two kinds of linear quadratic optimal control problems for multistage switched systems composing of both randomness and uncertainty are studied. Chance theory brings us a useful tool to deal with this indeterminacy. Based on chance theory and Bellman's principle, the analytical expressions are derived for calculating both the optimal control input and the optimal switching control law. Optimal control is implemented by genetic algorithm instead of enumerating all the elements of a series of sets whose size grows exponentially. Finally, the results of numerical examples are provided to illustrate the effectiveness of the proposed method.

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