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



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.


Hamilton–Jacobi–Bellman equation Minimal time function Subdifferential Time optimal control 

Mathematics Subject Classification

93C23 90C48 49J52 



This work was partially supported by National Natural Science Foundation of China (11201324), Fok Ying Tuny Education Foundation (141114), Outstanding Youth Academic Technology Leader Training Plan of Sichuan province (2013JQ0027), the Provost’s Chair Fund of National University of Singapore, and a research grant from Faculty of Science and Engineering, Curtin University.


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.VC/VR Lab and Department of MathematicsSichuan Normal UniversityChengduChina
  2. 2.Department of Decision Sciences, National University of Singapore and Department of Mathematics and StatisticsCurtin UniversityBentleyAustralia

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