Introduction and examples, optimal control problems governed by elliptic and parabolic systems, adjoint systems, optimality conditions, optimal control and optimality systems for other PDEs like Stokes systems.

Suggested books and references:

Fredi Troltzsch, Optimal control of partial differential equations; Theory, Methods and Applications
,Graduate Studies in Mathematics, Volume 112, AMS (2010).

J. L. Lions, Optimal control of systems governed by partial differential equations
,Springer Verlag, 1971.

J. L. Lions, Controlabilite exacte, perturbations et stabilisation de systems distribues, Tome 1 and 2
,Research in applied mathematics, Vol. 8 and 9, Masson, Paris, 1988.

V. Barbu, Mathematical methods in optimization of differential systems
,Mathematics and its applications, Vol. 310 Kluwer academic Publishers, 1994.