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Uncertain bang–bang control problem for multi-stage switched systems

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  • Yan, Hongyan
  • Jin, Ting
  • Sun, Yun

Abstract

A control problem for multi-stage switched systems with subsystems disturbed by uncertainty is presented. This problem is formulated as computing the optimal continuous input and the optimal switching strategy that jointly optimizes a linear performance index. Analytic expressions are derived for both of them. Enumeration method for solving such a control problem suffers a high computational requirement due to the fact that an exponential number of switching sequences must be explored. Genetic Algorithm is chosen to improve the computing efficiency. The examples validate the effectiveness of the method.

Suggested Citation

  • Yan, Hongyan & Jin, Ting & Sun, Yun, 2020. "Uncertain bang–bang control problem for multi-stage switched systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 551(C).
    • Handle: RePEc:eee:phsmap:v:551:y:2020:i:c:s0378437119322721
    DOI: 10.1016/j.physa.2019.124115
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    References listed on IDEAS

    as
    1. Hongyan Yan & Yuanguo Zhu, 2017. "Bang–bang control model with optimistic value criterion for uncertain switched systems," Journal of Intelligent Manufacturing, Springer, vol. 28(3), pages 527-534, March.
    2. Daniel Kahneman & Amos Tversky, 2013. "Prospect Theory: An Analysis of Decision Under Risk," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 6, pages 99-127, World Scientific Publishing Co. Pte. Ltd..
    3. Jin, Ting & Sun, Yun & Zhu, Yuanguo, 2019. "Extreme values for solution to uncertain fractional differential equation and application to American option pricing model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 534(C).
    4. Ziqiang Lu & Hongyan Yan & Yuanguo Zhu, 2019. "European option pricing model based on uncertain fractional differential equation," Fuzzy Optimization and Decision Making, Springer, vol. 18(2), pages 199-217, June.
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    Cited by:

    1. Chen, Xin & Zhu, Yuanguo & Sheng, Linxue, 2021. "Optimal control for uncertain stochastic dynamic systems with jump and application to an advertising model," Applied Mathematics and Computation, Elsevier, vol. 407(C).

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