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Proximal Analysis and the Minimal Time Function of a Class of Semilinear Control Systems

Author

Listed:
  • Yi Jiang

    (Sichuan Normal University)

  • Yiran He

    (Sichuan Normal University)

  • Jie Sun

    (Curtin University)

Abstract

The minimal time function of a class of semilinear control systems is considered in Banach spaces, with the target set being a closed ball. It is shown that the minimal time functions of the Yosida approximation equations converge to the minimal time function of the semilinear control system. Complete characterization is established for the subdifferential of the minimal time function satisfying the Hamilton–Jacobi–Bellman equation. These results extend the theory of finite dimensional linear control systems to infinite dimensional semilinear control systems.

Suggested Citation

  • Yi Jiang & Yiran He & Jie Sun, 2016. "Proximal Analysis and the Minimal Time Function of a Class of Semilinear Control Systems," Journal of Optimization Theory and Applications, Springer, vol. 169(3), pages 784-800, June.
    • Handle: RePEc:spr:joptap:v:169:y:2016:i:3:d:10.1007_s10957-015-0848-z
    DOI: 10.1007/s10957-015-0848-z
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    References listed on IDEAS

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    1. Yi Jiang & Yi He & Jie Sun, 2011. "Subdifferential properties of the minimal time function of linear control systems," Journal of Global Optimization, Springer, vol. 51(3), pages 395-412, November.
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