Riccati equations and LQ-optimal control for a class of hyperbolic PDEs

Anthony Hastir; Birgit Jacob; Hans Zwart

doi:10.48550/arXiv.2503.11602

Riccati equations and LQ-optimal control for a class of hyperbolic PDEs

Anthony Hastir
, Birgit Jacob
, Hans Zwart

Mathematical Systems Theory

Research output: Working paper › Preprint › Academic

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Abstract

We derive an explicit solution to the operator Riccati equation solving the Linear-Quadratic (LQ) optimal control problem for a class of boundary controlled hyperbolic partial differential equations (PDEs). Different descriptions of the system are used to obtain different representations of the operator Riccati equation. By means of an example, we illustrate the importance of considering an extended operator Riccati equation to solve the LQ-optimal control problem for our class of systems.

Original language	English
Publisher	ArXiv.org
DOIs	https://doi.org/10.48550/arXiv.2503.11602
Publication status	Published - 14 Mar 2025

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math.OC

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10.48550/arXiv.2503.11602

2503.11602v1Final published version, 195 KB

Riccati equations and LQ-optimal control for a class of hyperbolic PDEs
Hastir, A., Jacob, B. & Zwart, H., Nov 2025, In: Systems and control letters. 205, 106244.
Research output: Contribution to journal › Article › Academic › peer-review

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AB - We derive an explicit solution to the operator Riccati equation solving the Linear-Quadratic (LQ) optimal control problem for a class of boundary controlled hyperbolic partial differential equations (PDEs). Different descriptions of the system are used to obtain different representations of the operator Riccati equation. By means of an example, we illustrate the importance of considering an extended operator Riccati equation to solve the LQ-optimal control problem for our class of systems.

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Riccati equations and LQ-optimal control for a class of hyperbolic PDEs

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Riccati equations and LQ-optimal control for a class of hyperbolic PDEs

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