Koba Gelashvili

About a Simple Analytic Proof of Pontryagin's Maximum Principle

abstract:
Using compact expressions for optimal and varied trajectories based on the representation of the Cauchy problem solution as evolution system of functions of initial values, a simple analytic proof of Pontryagin's Maximum Principle for fixed endpoints is obtained. Some non-standard problems of optimal control theory are considered shortly, too.

Mathematics Subject Classification: 49K15.

Key words and phrases: Evolution system, Pontryagin's Maximum Principle, variable control area, admissible controls with uniformly limited number of points of discontinuity.