The asymptotics of the solutions of perturbed optimal control problems (Q1913075)

This is a short survey of the author's works published in 1987-1990 and devoted to the investigation of regular and singular perturbed optimal control problems. The author has considered problems with a closed control region such as time-optimal control problems and some optimal control problems with a free endpoint. The asymptotic iterational algorithms for constructing optimal solutions are developed and substantiated. The algorithms are based on theorems of the existence of optimal controls and Pontryagin extremals of specified structure proved for the considered perturbed problems. The question whether the solutions of the original and of the perturbed problems are closed has been considered. The developed methods can be used effectively for obtaining numerical solutions. Difficulties arising in the process of constructing the asymptotic expansions are discussed.