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Null controllability of an ODE-heat system coupled at boundary and internal term

Author

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  • Zeng, Caijin
  • Zhou, Zhongcheng
  • Xie, Chengkang

Abstract

In this article, the null controllability of a coupled ODE-heat system is considered by backstepping method. First, according to a backstepping transformation, the system is transferred into an intermediate system which has an equivalence of null controllability with the original system. Second, we divide the finite time interval into a sequence of time intervals, and on each time interval, transform the intermediate system into a target system through another backstepping transformation. Consequently, we obtain the crucial norm estimates of states and control laws. Finally, based on the invertibility of the target system, we prove null controllability of the intermediate system and ultimately, show the null controllability of the original coupled ODE-heat system. In addition, numerical experiment results are presented to examine the validity for the presented controller.

Suggested Citation

  • Zeng, Caijin & Zhou, Zhongcheng & Xie, Chengkang, 2024. "Null controllability of an ODE-heat system coupled at boundary and internal term," Applied Mathematics and Computation, Elsevier, vol. 475(C).
    • Handle: RePEc:eee:apmaco:v:475:y:2024:i:c:s0096300324001966
    DOI: 10.1016/j.amc.2024.128724
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    References listed on IDEAS

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    1. Hou, Mimi & Xi, Xuan-Xuan & Zhou, Xian-Feng, 2021. "Boundary control of a fractional reaction-diffusion equation coupled with fractional ordinary differential equations with delay," Applied Mathematics and Computation, Elsevier, vol. 406(C).
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