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: | Sun Jie, He Yiran, Jiang Yi |
Keywords: | optimization |
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.