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H∞ control for Poisson-driven stochastic systems

Author

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  • Song, Bo
  • Zhang, Ya
  • Park, Ju H.

Abstract

The paper aims to investigate the H∞ control problem for systems perturbed by jump random noise, i.e., Poisson-driven stochastic systems (SSs). Firstly, this paper uses the Doob-Meyer decomposition and measure theory to give a model transformation method, and Poisson-driven SSs, which are SSs driven by semi-martingale, are transformed into SSs driven by compensated Poisson process. Since SSs driven by compensated Poisson process are SSs driven by martingale, we can use effective properties and tools in martingale theory to investigate the H∞ control problem. Secondly, this paper utilizes martingale theory to deal with the jump item and the sum of stochastic integrals (SIs) with respect to (w.r.t.) the continuous part of states in Itô formula, and then gives an equivalent Itô formula for SDEs driven by compensated Poisson process. Thirdly, on the basis of these, this paper presents a simple H∞ controller design method. Furthermore, the design criterion contains information about the average number of jump random events in a unit time, and one can utilize convex optimization algorithm to estimate the maximum average number of jump random events in a unit time, which the closed-loop system can tolerate to achieve the stability and H∞ performance. Finally, the usefulness of the design result is verified by two numerical examples.

Suggested Citation

  • Song, Bo & Zhang, Ya & Park, Ju H., 2021. "H∞ control for Poisson-driven stochastic systems," Applied Mathematics and Computation, Elsevier, vol. 392(C).
    • Handle: RePEc:eee:apmaco:v:392:y:2021:i:c:s009630032030669x
    DOI: 10.1016/j.amc.2020.125716
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    References listed on IDEAS

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    1. Aghion, Philippe & Howitt, Peter, 1992. "A Model of Growth through Creative Destruction," Econometrica, Econometric Society, vol. 60(2), pages 323-351, March.
    2. Xu, Yong & Pei, Bin & Guo, Guobin, 2015. "Existence and stability of solutions to non-Lipschitz stochastic differential equations driven by Lévy noise," Applied Mathematics and Computation, Elsevier, vol. 263(C), pages 398-409.
    3. Kang, Ting & Li, Qiang & Zhang, Qimin, 2019. "Numerical analysis of the balanced implicit method for stochastic age-dependent capital system with poisson jumps," Applied Mathematics and Computation, Elsevier, vol. 353(C), pages 166-177.
    4. Yan, Zhiguo & Park, Ju H. & Zhang, Weihai, 2018. "A unified framework for asymptotic and transient behavior of linear stochastic systems," Applied Mathematics and Computation, Elsevier, vol. 325(C), pages 31-40.
    5. Gao, Rong, 2019. "Stability in mean for uncertain differential equation with jumps," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 15-22.
    6. Steger, Thomas M., 2005. "Stochastic growth under Wiener and Poisson uncertainty," Economics Letters, Elsevier, vol. 86(3), pages 311-316, March.
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