Necessary Conditions in Optimal Control Theory

Nico Tauchnitz

Published 2016-10-10Version 1

In this manuscript we develop necessary optimality conditions for weak and strong minimizer in control problems on finite and infinite horizon. We show, that the control problems on the infinite horizon are proper generalizations of the finite horizon problems. Therefore, we have to develop an innovative theoretical approach. The first chapters are devoted to known results and methods for weak and strong minimizer in finite horizon optimal control problems. In the last parts we extend these methods to infinite horizon problems. The chief task is the comprehension of the infinite horizon as a singularity in any element of the control problem. This singularity is not included in the classical control problems with finite horizon. Hence we have to verify, reconsider and enhance all known arguments and methods for finite horizon optimal control problems.