Abstract: The Jordan–Moore–Gibson–Thompson equation is a prominent example of a Partial Differential Equation model which describes the acoustic velocity potential in ultrasound wave propagation, and where the paradox of infinite speed of propagation of thermal signals is eliminated; the use of the constitutive Cattaneo law for the heat flux, in place of the Fourier law, accounts for its being of third order in time. A great deal of attention has been recently devoted to its linearization – referred to in the literature as the Moore–Gibson–Thompson equation – whose analysis poses already several questions and mathematical challenges. In this work, we consider and solve a quadratic control problem associated with the linear equation, formulated consistently with the goal of keeping the acoustic pressure close to a reference pressure during ultrasound excitation, as required in medical and industrial applications. While optimal control problems with smooth controls have been considered in the recent literature, we aim at relying on controls which are just square integrable in time; this leads to a singular control problem and to non-standard Riccati equations.

Feedback control of the acoustic pressure in ultrasonic wave propagation / Francesca Bucci; Irena Lasiecka. - In: OPTIMIZATION. - ISSN 0233-1934. - STAMPA. - 68 (Early access: August 2018):(2019), pp. 1811-1854. [10.1080/02331934.2018.1504051]

Feedback control of the acoustic pressure in ultrasonic wave propagation

Francesca Bucci
;
2019

Abstract

Abstract: The Jordan–Moore–Gibson–Thompson equation is a prominent example of a Partial Differential Equation model which describes the acoustic velocity potential in ultrasound wave propagation, and where the paradox of infinite speed of propagation of thermal signals is eliminated; the use of the constitutive Cattaneo law for the heat flux, in place of the Fourier law, accounts for its being of third order in time. A great deal of attention has been recently devoted to its linearization – referred to in the literature as the Moore–Gibson–Thompson equation – whose analysis poses already several questions and mathematical challenges. In this work, we consider and solve a quadratic control problem associated with the linear equation, formulated consistently with the goal of keeping the acoustic pressure close to a reference pressure during ultrasound excitation, as required in medical and industrial applications. While optimal control problems with smooth controls have been considered in the recent literature, we aim at relying on controls which are just square integrable in time; this leads to a singular control problem and to non-standard Riccati equations.
2019
68 (Early access: August 2018)
1811
1854
Goal 17: Partnerships for the goals
Francesca Bucci; Irena Lasiecka
File in questo prodotto:
File Dimensione Formato  
2018-optimization_feedbackcontrol.pdf

Accesso chiuso

Descrizione: Articolo
Tipologia: Pdf editoriale (Version of record)
Licenza: Tutti i diritti riservati
Dimensione 3.12 MB
Formato Adobe PDF
3.12 MB Adobe PDF   Richiedi una copia
Bucci-Lasiecka-sentrevision_jul18.pdf

accesso aperto

Descrizione: Articolo
Tipologia: Versione finale referata (Postprint, Accepted manuscript)
Licenza: Tutti i diritti riservati
Dimensione 385.19 kB
Formato Adobe PDF
385.19 kB Adobe PDF

I documenti in FLORE sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/1117447
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 25
  • ???jsp.display-item.citation.isi??? 23
social impact