Taylor Expansions of the Value Function Associated with a Bilinear Optimal Control Problem
Optimization and Control
2017-06-19 v1
Abstract
A general bilinear optimal control problem subject to an infinite-dimensional state equation is considered. Polynomial approximations of the associated value function are derived around the steady state by repeated formal differentiation of the Hamilton-Jacobi-Bellman equation. The terms of the approximations are described by multilinear forms, which can be obtained as solutions to generalized Lyapunov equations with recursively defined right-hand sides. They form the basis for defining a suboptimal feedback law. The approximation properties of this feedback law are investigated. An application to the optimal control of a Fokker-Planck equation is also provided.
Cite
@article{arxiv.1706.05341,
title = {Taylor Expansions of the Value Function Associated with a Bilinear Optimal Control Problem},
author = {Tobias Breiten and Karl Kunisch and Laurent Pfeiffer},
journal= {arXiv preprint arXiv:1706.05341},
year = {2017}
}