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

Yi Jiang (), Yiran He () and Jie Sun ()
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Yi Jiang: Sichuan Normal University
Yiran He: Sichuan Normal University
Jie Sun: Curtin University

Journal of Optimization Theory and Applications, 2016, vol. 169, issue 3, No 5, 784-800

Abstract: 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.

Keywords: Hamilton–Jacobi–Bellman equation; Minimal time function; Subdifferential; Time optimal control; 93C23; 90C48; 49J52 (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s10957-015-0848-z

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