Exponential Convergence of an Observer Based on Partial Field Measurements for the Wave Equation. (25th October 2012)

• Record Type: Journal Article
• Authors: Chapelle, Dominique; Cîndea, Nicolae; De Buhan, Maya; Moireau, Philippe
• Other Names: Yakhno Valery Academic Editor.
• Is Part Of: Mathematical problems in engineering. Volume 2012(2012)
• Publication Date: 2012-10-25
• Subjects: Engineering mathematics -- Periodicals; 510.2462
• DOI: 10.1155/2012/581053
• Languages: English
• ISSNs: 1024-123X

Abstract

Abstract : We analyze an observer strategy based on partial—that is, in a subdomain—measurements of the solution of a wave equation, in order to compensate for uncertain initial conditions. We prove the exponential convergence of this observer under a nonstandard observability condition, whereas using measurements of the time derivative of the solution would lead to a standard observability condition arising in stabilization and exact controlabillity. Nevertheless, we directly relate our specific observability condition to the classical geometric control condition. Finally, we provide some numerical illustrations of the effectiveness of the approach.