<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>The Moore-Gibson-Thompson [MGT] dynamics is considered. This third order in time evolution arises within the context of acoustic wave propagation with applications in high frequency ultrasound technology. The optimal boundary feedback control is constructed in order to have on-line regulation. The above requires wellposedness of the associated Algebraic Riccati Equation. The paper by Lasiecka and Triggiani (2022) recently contributed a comprehensive study of the Optimal Control Problem for the MGT-third order dynamics with boundary control, over an infinite time-horizon. A critical missing point in such a study is the issue of uniqueness (within a specific class) of the corresponding highly non-standard Algebraic Riccati Equation. The present note resolves this problem in the positive, thus completing the study of Lasiecka and Triggiani (2022) with the final goal of having on line feedback control, which is also optimal.</p>
</abstract>

The Moore-Gibson-Thompson [MGT] dynamics is considered. This third order in time evolution arises within the context of acoustic wave propagation with applications in high frequency ultrasound technology. The optimal boundary feedback control is constructed in order to have on-line regulation. The above requires wellposedness of the associated Algebraic Riccati Equation. The paper by Lasiecka and Triggiani (2022) recently contributed a comprehensive study of the Optimal Control Problem for the MGT-third order dynamics with boundary control, over an infinite time-horizon. A critical missing point in such a study is the issue of uniqueness (within a specific class) of the corresponding highly non-standard Algebraic Riccati Equation. The present note resolves this problem in the positive, thus completing the study of Lasiecka and Triggiani (2022) with the final goal of having on line feedback control, which is also optimal.

Uniqueness of the Riccati operator of the non-standard ARE of a third order dynamics with boundary control

Control and Cybernetics

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

The Moore-Gibson-Thompson [MGT] dynamics is considered. This third order in time evolution arises within the context of acoustic wave propagation with...

Uniqueness of the Riccati operator of the non-standard ARE of a third order dynamics with boundary control

Published Online: Aug 12, 2022

Page range: 171 - 189

Received: Mar 01, 2022

Accepted: May 01, 2022

DOI: https://doi.org/10.2478/candc-2022-0013

Keywords
uniqueness, non-standard algebraic Riccati equation, Moore-Gibson-Thompson equation

© 2022 Irena Lasiecka et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Uniqueness of the Riccati operator of the non-standard ARE of a third order dynamics with boundary control

Published Online: Aug 12, 2022

Page range: 171 - 189

Received: Mar 01, 2022

Accepted: May 01, 2022

DOI: https://doi.org/10.2478/candc-2022-0013

Keywordsuniqueness, non-standard algebraic Riccati equation, Moore-Gibson-Thompson equation

© 2022 Irena Lasiecka et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
uniqueness, non-standard algebraic Riccati equation, Moore-Gibson-Thompson equation