Conditions for strict dissipativity of infinite-dimensional generalized linear-quadratic problems

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Grüne, Lars ; Muff, David ; Schaller, Manuel:
Conditions for strict dissipativity of infinite-dimensional generalized linear-quadratic problems.
Bayreuth ; Ilmenau , 2021 . - 9 S.

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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.