Optimal control problem on an unbounded interval (Q1608122)

The author proves the Pontryagin maximum principle for optimal control problems on an unbounded interval, constraints being of an inequality and an equality type. Problems are considered in the general class of admissible controls as in the classical work [\textit{L. S. Pontryagin}, \textit{V. G. Boltyanskiĭ}, \textit{R. V. Gamkrelidze} and \textit{E. F. Mishchenko}, ``Mathematical theory of optimal processes.'' (Russian) Moscow: FizMatLit (1961; Zbl 0102.31901)]. A control is a function that maps an interval (bounded or unbounded) into a topological space. A class of measurable admissible controls is derived. The proof of the maximum principle is carried out by using the not accurate notion of measurability introduced by the author in [``Needle variation'', J. Math. Sci., New York 110, No. 2, 2558--2571 (2002; Zbl 1018.49014)] and the tent theory given by the author in [``Tent theory'', J. Math. Sci., New York 110, 2572--2582 (2002; Zbl 1018.49014)].