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

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

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Article ID: iaor20162405
Volume: 169
Issue: 3
Start Page Number: 784
End Page Number: 800
Publication Date: Jun 2016
Journal: Journal of Optimization Theory and Applications
Authors: , ,
Keywords: optimization
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.

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