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

Anthony Hastir; Birgit Jacob; Hans Zwart

doi:10.1016/j.sysconle.2025.106244

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

Anthony Hastir
, Birgit Jacob
, Hans Zwart^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › Academic › peer-review

2 Citations (Scopus)

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) defined on a one-dimensional spatial domain. 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
Article number	106244
Journal	Systems and control letters
Volume	205
DOIs	https://doi.org/10.1016/j.sysconle.2025.106244
Publication status	Published - Nov 2025

Keywords

Hyperbolic PDEs
LQ-optimal control
Riccati equations
Spectral factorization
Unbounded input and output operators

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10.1016/j.sysconle.2025.106244

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title = "Riccati equations and LQ-optimal control for a class of hyperbolic PDEs",

abstract = "We derive an explicit solution to the operator Riccati equation solving the Linear{\textendash}Quadratic (LQ) optimal control problem for a class of boundary controlled hyperbolic partial differential equations (PDEs) defined on a one-dimensional spatial domain. 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.",

keywords = "Hyperbolic PDEs, LQ-optimal control, Riccati equations, Spectral factorization, Unbounded input and output operators",

author = "Anthony Hastir and Birgit Jacob and Hans Zwart",

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year = "2025",

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doi = "10.1016/j.sysconle.2025.106244",

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T1 - Riccati equations and LQ-optimal control for a class of hyperbolic PDEs

AU - Hastir, Anthony

AU - Jacob, Birgit

AU - Zwart, Hans

PY - 2025/11

Y1 - 2025/11

N2 - 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) defined on a one-dimensional spatial domain. 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.

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) defined on a one-dimensional spatial domain. 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.

KW - Hyperbolic PDEs

KW - LQ-optimal control

KW - Riccati equations

KW - Spectral factorization

KW - Unbounded input and output operators

UR - https://www.scopus.com/pages/publications/105016528148

U2 - 10.1016/j.sysconle.2025.106244

DO - 10.1016/j.sysconle.2025.106244

M3 - Article

AN - SCOPUS:105016528148

SN - 0167-6911

VL - 205

JO - Systems and control letters

JF - Systems and control letters

M1 - 106244

ER -

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

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Keywords

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

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