1. Introduction: Optimal control and controllability. Exemples in finite and infinite dimension
2. Control of the finite dimensional systems: Necessary and sufficient conditions for controllability
Variational methods to find the control
3. Controllability in one dimension with Fourier series: Riesz basis. Biorthogonal sequences.
Applications to the controllability of the wave and heat equation.
4. Controllability of the wave and heat equation in several dimensions:
Unique continuation principle. Approximate controllability.
Hilbert Uniqueness Method (HUM)
5. Stabilizability of the wave equation:
Problem of stabilizability for the wave equation.
Relation between stabilizability and controllability
1. S.A. Avdonin and S.A. Ivanov, Families of exponentials.
The method of moments in controlability problems for distributed parameter systems,
Cambridge Univ. Press, 1995.
2. T. Cazenave and A. Haraux, Introduction aux problemes d’evolution semi-lineaires,
Mathematiques et Applications, 1, Ellipses, Paris, 1990.
3. E.B.Lee and L. Marcus, Foundation of Optimal Control Theory,
The SIAM Series in Applied Mathematics, John Wiley &Sons, 1967.
4. J.L. Lions, Controlabilite exacte, perturbations et stabilisations de systemes distribues,
Vol.1&2, Masson, RMA, Paris, 1988.
5. R. Young, An Introduction to Nonharmonic Fourier Series, Academic Press, 1980.