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Adaptive Parameter Estimation of Hyperbolic Distributed Parameter Systems: Non-symmetric Damping and Slowly Time Varying Systems

H. T. Banks, M. A. Demetriou (2010)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper a model reference-based adaptive parameter estimator for a wide class of hyperbolic distributed parameter systems is considered. The proposed state and parameter estimator can handle hyperbolic systems in which the damping sesquilinear form may not be symmetric (or even present) and a modification to the standard adaptive law is introduced to account for this lack of symmetry (or absence) in the damping form. In addition, the proposed scheme is modified for systems in which the input...

Exact controllability of the wave equation with mixed boundary condition and time-dependent coefficients

M. M. Cavalcanti (1999)

Archivum Mathematicum

In this paper we study the boundary exact controllability for the equation t α ( t ) y t - j = 1 n x j β ( t ) a ( x ) y x j = 0 in Ω × ( 0 , T ) , when the control action is of Dirichlet-Neumann form and Ω is a bounded domain in R n . The result is obtained by applying the HUM (Hilbert Uniqueness Method) due to J. L. Lions.

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