Asymptotic controllability for linear hyperbolic systems

Article type: Research Article

Authors: Li, Tatsien | Rao, Bopeng

Affiliations: Shanghai Key Laboratory for Contemporary Applied Mathematic and Nonlinear Mathematical Modeling and Methods Laboratory, School of Mathematical Sciences, Fudan University, Shanghai 200433, China. E-mail: dqli@fudan.edu.cn | Institut de Recherche Mathématique Avancée, Université de Strasbourg, 67084 Strasbourg, France. E-mail: bopeng.rao@math.unistra.fr

Abstract: For 1-D linear hyperbolic systems with constant coefficients we introduce the asymptotic controllability and the asymptotic zero controllability in L2 space under the lack of boundary controls and show the duality that they are equivalent, respectively, to the strong observability and the weak observability for the dual system. An example of 4×4 system with only one control is shown to be asymptotically controllable but not exactly controllable.

Keywords: linear hyperbolic system, asymptotic (zero) controllability, exact controllability, strong (weak) observability

DOI: 10.3233/ASY-2010-1027

Journal: Asymptotic Analysis, vol. 72, no. 3-4, pp. 169-187, 2011