Conditions for strict dissipativity of infinite-dimensional generalized linear-quadratic problems
Optimization and Control
2021-07-27 v2
Abstract
We derive sufficient conditions for strict dissipativity for optimal control of linear evolution equations on Hilbert spaces with a cost functional including linear and quadratic terms. We show that strict dissipativity with a particular storage function is equivalent to ellipticity of a Lyapunov-like operator. Further we prove under a spectral decomposition assumption of the underlying generator and an orthogonality condition of the resulting subspaces that this ellipticity property holds under a detectability assumption. We illustrate our result by means of an example involving a heat equation on a one-dimensional domain.
Cite
@article{arxiv.2104.10072,
title = {Conditions for strict dissipativity of infinite-dimensional generalized linear-quadratic problems},
author = {Lars Grüne and David Muff and Manuel Schaller},
journal= {arXiv preprint arXiv:2104.10072},
year = {2021}
}