文章基本信息

标题：Conditions for strict dissipativity of infinite-dimensional generalized linear-quadratic problems ⁎
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作者：Lars Grüne ; David Muff ; Manuel Schaller 等
期刊名称：IFAC PapersOnLine
印刷版ISSN：2405-8963
出版年度：2021
卷号：54
期号：19
页码：302-306
DOI：10.1016/j.ifacol.2021.11.094
语种：English
出版社：Elsevier
摘要：AbstractWe 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.
关键词：Keywordsoptimal controldissipativityinfinite-dimensional systemdetectabilityellipticityLyapunov inequalitynecessary optimality condition