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Optimal control for uncertain discrete-time singular systems under expected value criterion

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Abstract

Optimal control problems governed by two different types of uncertain discrete-time singular systems are investigated under expected value criterion. The objective function including uncertain variables is optimized with the help of expected value method provided that the singular systems are both regular and impulse-free. At first, based on the principle of dynamic programming, a recurrence equation is derived to simplify an optimal control model for a class of uncertain discrete-time singular systems. After that, according to uncertainty theory and the recurrence equation, two kinds of optimal control problems subject to an uncertain linear singular system and an uncertain singular system with quadratic input variables are considered in order, and the optimal solutions are both presented by accurate expressions. A numerical example and a dynamic input-output model are settled to illustrate the effectiveness of the results obtained.

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Acknowledgements

This work is supported by the Startup Foundation for Introducing Talent of NUIST (No. 2018r097) and the National Natural Science Foundation of China (No. 61673011).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing, 210044, China

    Yadong Shu

  2. School of Applied Mathematics, Nanjing University of Finance and Economics, Nanjing, 210023, China

    Bo Li

  3. School of Science, Nanjing University of Science and Technology, Nanjing, 210094, China

    Yuanguo Zhu

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  1. Yadong Shu
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  2. Bo Li
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  3. Yuanguo Zhu
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Correspondence to Yadong Shu.

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Shu, Y., Li, B. & Zhu, Y. Optimal control for uncertain discrete-time singular systems under expected value criterion. Fuzzy Optim Decis Making 20, 331–364 (2021). https://doi.org/10.1007/s10700-020-09346-5

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