The study of optimal control
problems is by now well developed and with advances in several
directions. The Maximum Principle of Pontryagin, a set of necessary
conditions for optimality of a control function, has been continuously
improved to include different and new types of constraints and to allow
less regularity on the data of the problem. In that way the class of
problems to which such Maximum Principle can be applied has becoming
larger.
In this presentation the focus will be on the Maximum
Principle from its classical form to a more sophisticated one where
state constraints are involved. Other main issues related to an optimal
control problem are discussed as well as some main research directions. |