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

• Autorzy: Lasiecka Irena , Triggiani Roberto

Identyfikatory

DOI

10.2478/candc-2022-0013

• Języki publikacji: EN

Abstrakty

EN

TheMoore-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.

Słowa kluczowe

EN

uniqueness; non-standard algebraic Riccati equation; Moore-Gibson-Thompson equation

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2022
• Tom: Vol. 51, No. 2
• Strony: 171--189
• Opis fizyczny: Bibliogr. 27 poz., rys.

Twórcy

autor

Lasiecka Irena

• Department of Mathematical Sciences, University of Memphis, Memphis, TN, USA 38152
• Systems Research Institute, Polish Academy of Sciences, Newelska 6, 01447 Warszawa, Poland

autor

Triggiani Roberto

• Department of Mathematical Sciences, University of Memphis, Memphis, TN, USA 38152

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