After successful completion of the course, students are able to formulate various types of optimal control models, to obtain complete systems of optimality conditions and to analyze qualitative properties of the solutions.

The dynamic optimization deals with optmization of processes, that is of systems that change with the time. Itertemporal decision processes play an important role in economics, operations research and technicsboth as (i) efficient tools for decision making or for finding efficient engeneering solutions, and (ii) for qualitative analysis. The dynamics of such systems is usually described by differential or difference equations, accompanied with additional (static) constraints. The course will begin with several examples from economics and technics,which will be used later for illustration of the theory. Then two approaches (a geometric and an analytic ones) for obtaining optimality conditions for simple classes of optimal control problems will be presented. An idea of how these approaches can be unified and extended in order to cope with more complicated problems will be given. As a result the Pontryagin maximum principle will be obtained for several classes of problems and its relationship with other optimality conditions will be discussed. Several classical economic models and modelsfor management of renewable resources will be analysed, as well as models arizing in technics, epidemiology and sociology.

Lectures and exercises.

Oral examination