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arXiv · 2603.24507

Optimal control of infinite-dimensional dissipative systems

Anthony Hastir·Timo Reis
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Abstract

We study the linear-quadratic optimal control problem for infinite-dimensional dissipative systems with possibly indefinite cost functional. Under the assumption that a storage function exists, we show that this indefinite optimal control problem is equivalent to a linear-quadratic optimal control problem with a nonnegative cost functional. We establish the relationship between the corresponding value functions and present the associated operator Lur'e equation. Finally, we illustrate our results with several examples.

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Anthony Hastir, Timo Reis. 2026-03-25. Optimal control of infinite-dimensional dissipative systems. https://arxiv.org/abs/2603.24507

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