CONTROL AND HOMOGENIZATION
Prerequisites:Sobolev spaces, Elliptic boundary value problems, Heat and wave equations, Variational formulation and semigroup theory. Optimal Control of PDE:Optimal control problems governed by elliptic equations and linear parabolic and hyperbolic equations with distributed and boundary controls, Computational methods. Homogenization:Examples of periodic composites and layered materials. Various methods of homogenization. Applications and Extensions:Control in coefficients of elliptic equations, Controllability and Stabilization of Infinite Dimensional Systems, Hamilton- Jacobi-Bellman equations and Riccati equations, Optimal control and stabilization of flow related models.
Books
- B. Lee and L. Markus, Foundations of Optimal Control Theory, John Wiley, 1968.
- L. Lions, Optimal Control of Systems Governed by Partial Differential Equations, Springer, 1991.
- L. Lions, Controlabilite exact et Stabilisation des systemes distribues, Vol. 1, 2 Masson, Paris 1988.
- Bardi, I. Capuzzo-Dolcetta, Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations, Birkhauser, 1997.
- Kesavan, Topics in Functional Analysis and Applications, Wiley-Eastern, New Delhi, 1989.
- Dal Maso, An Introduction to $\Gamma$-Convergence, Birkhauser, 1993.