[For the entire collection see Zbl 0605.00020.] At first convergence of solutions and some estimates are established for singularly perturbed nonlinear optimal control problems with control constraints and convexity. Secondly, for linear quadratic problems and for nonlinear problems without control constraints, it is shown that asymptotic expansions of the solutions of the corresponding necessary optimality conditions lead to a direct expansion of the cost function in the perturbed problem. Reviewer’s remark: Analogous results starting from a direct expansion of the necessary optimality conditions for the perturbed problem and using boundary layer functions as well as the successive solution of lower- dimensional approximate decomposition problems have been obtained by {\it S. V. Belokopytov} and the reviewer [Izv. Akad. Nauk SSSR, Tekh. Kibern. 1985, No.3, 147-152 (1985; Zbl 0585.49018); and Syst. Control Lett. 8, 129-135 (1986; Zbl 0609.49022)]. Finally, the author considers the expansion of the solution of Bellman’s equation and the questions connected with the construction of composite feedback in infinite horizon problems.
Reviewer: M.Dmitriev