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Controllability of Partial Differential Equations

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Figure 3.1: Wave localized at t = 0 near the endpoint x = 1 that propagates with velocity 1 to the left, bounces at x = 0 and reaches x = 1 again in a time of the order of 2.
Figure 3.2: Ray that propagates inside the domain Ω following straight lines that are reflected on the boundary according to the laws of geometrical optics.
Figure 3.3: A geometric configuration in which the Geometric Control Condi- Condi-tion is not satisfied, whatever T > 0 is
Figure 3.4: Square roots of the eigenvalues in the continuous and discrete case.

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Controllability of linear finite dimensional systems Controllability of nonlinear finite dimensional systems Control, complexity and numerical simulation Controllability of finite dimensional linear systems Controllability and the problem of moments Estimate of the norm of the biorthogonal sequence: T = ∞143 Non uniform observability Fourier Filtering Conclusion and controllability results

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