Linear-quadratic optimal control for abstract differential-algebraic equations
Abstract
In this paper, we extend a classical approach to linear quadratic (LQ) optimal control via Popov operators to abstract linear differential-algebraic equations (ADAEs) in Hilbert spaces. To ensure existence of solutions, we assume that the underlying differential-algebraic equation has index one in the pseudo-resolvent sense. This leads to the existence of a degenerate semigroup that can be used to define a Popov operator for our system. It is shown that under a suitable coercivity assumption for the Popov operator the optimal costs can be described by a bounded Riccati operator and that the optimal control input is of feedback form. Furthermore, we characterize exponential stability of ADAEs which is required to solve the infinite horizon LQ problem.
Cite
@article{arxiv.2402.08762,
title = {Linear-quadratic optimal control for abstract differential-algebraic equations},
author = {Hannes Gernandt and Timo Reis},
journal= {arXiv preprint arXiv:2402.08762},
year = {2024}
}