Optimal control of infinite-dimensional dissipative systems

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.

Source: arXiv:2603.24507v1 - http://arxiv.org/abs/2603.24507v1 PDF: https://arxiv.org/pdf/2603.24507v1 Original Link: http://arxiv.org/abs/2603.24507v1