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LQ optimal control of fractional-order discrete-time uncertain systems

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  • Lu, Qinyun
  • Zhu, Yuanguo

Abstract

This paper primarily focuses on LQ optimal control problem of fractional-order discrete-time systems based on uncertainty theory that is a significant tool to model belief degree. First, an equivalent LQ problem, which is integer-order one, is presented by expanding the state variables with the unchanging control variables. This equivalent problem is then solved by dynamic programming approach. Accordingly, the solution of the proposed LQ optimal control problem reduces to solve a system of backward matrix difference equations. Finally, a numerical example is provided to show how to solve the proposed LQ optimal control problem. As an application, an LQ optimal control problem of macroeconomic system is discussed by the achieved results.

Suggested Citation

  • Lu, Qinyun & Zhu, Yuanguo, 2021. "LQ optimal control of fractional-order discrete-time uncertain systems," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    • Handle: RePEc:eee:chsofr:v:147:y:2021:i:c:s0960077921003386
    DOI: 10.1016/j.chaos.2021.110984
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    1. Škovránek, Tomáš & Podlubny, Igor & Petráš, Ivo, 2012. "Modeling of the national economies in state-space: A fractional calculus approach," Economic Modelling, Elsevier, vol. 29(4), pages 1322-1327.
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    3. Lu, Ziqiang & Zhu, Yuanguo, 2019. "Numerical approach for solution to an uncertain fractional differential equation," Applied Mathematics and Computation, Elsevier, vol. 343(C), pages 137-148.
    4. Jin, Ting & Zhu, Yuanguo, 2020. "First hitting time about solution for an uncertain fractional differential equation and application to an uncertain risk index model," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).
    5. Lu, Ziqiang & Zhu, Yuanguo & Li, Bo, 2019. "Critical value-based Asian option pricing model for uncertain financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 694-703.
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    Cited by:

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    2. Danca, Marius-F., 2022. "Fractional order logistic map: Numerical approach," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).

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