The Fundamental Solution and Its Role in the Optimal Control of Infinite Dimensional Neutral Systems |
| |
Authors: | Kai Liu |
| |
Institution: | (1) Division of Statistics and Probability, Department of Mathematical Sciences, The University of Liverpool, Peach Street, L69 7ZL Liverpool, UK |
| |
Abstract: | In this work, we shall consider standard optimal control problems for a class of neutral functional differential equations
in Banach spaces. As the basis of a systematic theory of neutral models, the fundamental solution is constructed and a variation
of constants formula of mild solutions is established. We introduce a class of neutral resolvents and show that the Laplace
transform of the fundamental solution is its neutral resolvent operator. Necessary conditions in terms of the solutions of
neutral adjoint systems are established to deal with the fixed time integral convex cost problem of optimality. Based on optimality
conditions, the maximum principle for time varying control domain is presented. Finally, the time optimal control problem
to a target set is investigated. |
| |
Keywords: | Neutral functional differential equation Fundamental solution Neutral resolvent operator Optimal control |
本文献已被 SpringerLink 等数据库收录! |
|