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. |