Constrained Optimal Control Problems

Abstract

In Chapter 5, we have shown how Optimal Control could be developed from the Calculus of Variations, presented Pontryagin’s Maximum Principle and discussed the Transversality conditions for the various cases, both in finite and infinite horizon problems. The second variations and sufficiency conditions have also been examined. In this chapter, we shall continue the exposition of the Optimal Control theory, concentrating on the point, differential equation and isoperimetric equality constraints as well as the control and state variables inequality constraints. Some economic applications will be presented. Finally, Dynamic Programming, Hamilton Jacobi equation and Euler equations will be briefly related to one another. We shall continue to use the results obtained from the Calculus of Variations to save lengthy discussions.