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Volume 8 Issue 12
Dec.  2021

IEEE/CAA Journal of Automatica Sinica

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Article Navigation >  IEEE/CAA Journal of Automatica Sinica  > 2021  >  8(12): 1956-1963
Z. Q. Ge, "Exact Controllability and Exact Observability of Descriptor Infinite Dimensional Systems," IEEE/CAA J. Autom. Sinica, vol. 8, no. 12, pp. 1956-1963, Dec. 2021. doi: 10.1109/JAS.2020.1003411
Citation: Z. Q. Ge, "Exact Controllability and Exact Observability of Descriptor Infinite Dimensional Systems," IEEE/CAA J. Autom. Sinica, vol. 8, no. 12, pp. 1956-1963, Dec. 2021. doi: 10.1109/JAS.2020.1003411
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Exact Controllability and Exact Observability of Descriptor Infinite Dimensional Systems

doi: 10.1109/JAS.2020.1003411

  • School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an 710049, China

Funds:  This work was supported by the National Natural Science Foundation of China (11926402, 61973338)
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    Abstract
  • Necessary and sufficient conditions for the exact controllability and exact observability of a descriptor infinite dimensional system are obtained in the sense of distributional solution. These general results are used to examine the exact controllability and exact observability of the Dzektser equation in the theory of seepage and the exact controllability of wave equation.

     

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    Highlights

    • The difference between the impulsive solution and the mild solution is explained, which shows the difference between the exact controllability in the sense of the two solutions.
    • The dual principle holds in the sense of impulsive solution but not in the sense of mild solution.
    • The example shows that the approximate controllable system is not necessarily exactly controllable.
    • For a specific descriptor infinite dimensional system, appropriate controllability can be defined according to the needs of various optimal control problems.

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