Linear-quadratic optimal control for infinite-dimensional input-state-output systems

Authors

Timo Reis, Manuel Schaller

Abstract

We examine the minimization of a quadratic cost functional composed of the output and the terminal state of infinite-dimensional evolution equations in view of existence of solutions and optimality conditions. While the initial value is prescribed, we are minimizing over all inputs within a specified convex subset of square integrable controls with values in a Hilbert space. The considered class of infinite-dimensional systems is based on the system node formulation. Thus, our developed approach includes optimal control of a wide variety of linear partial differential equations with boundary control and observation that are not well-posed in the sense that the output continuously depends on the input and the initial value. We provide an application of particular optimal control problems arising in energy-optimal control of port-Hamiltonian systems. Last, we illustrate the our theory by two examples including a non-well-posed heat equation with Dirichlet boundary control and a wave equation on an L-shaped domain with boundary control of the stress in normal direction.

Citation

• Journal: ESAIM: Control, Optimisation and Calculus of Variations
• Year: 2025
• Volume: 31
• Issue:
• Pages: 36
• Publisher: EDP Sciences
• DOI: 10.1051/cocv/2025026

BibTeX

@article{Reis_2025,
  title={{Linear-quadratic optimal control for infinite-dimensional input-state-output systems}},
  volume={31},
  ISSN={1262-3377},
  DOI={10.1051/cocv/2025026},
  journal={ESAIM: Control, Optimisation and Calculus of Variations},
  publisher={EDP Sciences},
  author={Reis, Timo and Schaller, Manuel},
  year={2025},
  pages={36}
}

Download the bib file

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