Optimal control problems with free right end point

Abstract

This paper is dedicated to the elementary proof of Pontryagin's maximum principle for problems with free right end point. The proof for the standard problem is taken from the monography of Ioffe and Tichomirov. We assume piecewise continuous controls and the proof turns out to be very simple. We generalize the concept to the problem of optimal multiprocesses, to control problems with delays and to the control of Volterra integral equations. Furthermore, we discuss the problem on infinite horizon. Moreover, we state Arrow type sufficiency conditions. The optimality conditions are demonstrated on illustrative examples.