An approximate optimal control for discrete models: Its design

Constructive schemes for designing approximate optimal controls based on the Krotov sufficient conditions of optimality, extension principle, and global estimation are described. Different approximations for Bellman-type relations and effective indirect schemes based on degeneracy and turnpike nature of solutions of applied problems are studied. Irrespective of the initial formulation of a problem, discrete-time models (exact or approximate models obtained from discretization of the initial model) are used in the final design stage. Examples are given.