On the synthesis problem for optimal control systems

A new approach to the synthesis problem of optimal controls of feedback typ e is considered. Algorithms of operating optimal controllers which are able to calculate values of optimal feedbacks during each particular control pr ocess in real time are described. The algorithm of operating the controller of the rst type ( continuous controller) is based on solving special (defi ning) equations in real time using the Newton method. For operating the opt imal controller of the second type (discrete controller) the dual method of linear programming is used. In control problems for systems under uncertai nty, a nonstochastic model is used, around which guaranteed results are obt ained. Under incomplete and inexact information, problems of optimal observ ation and identification are introduced. Algorithms of operating the optima l estimator and identifier which are able to construct estimates of availab le information required for operating the optimal output controller in real time are described. Results are illustrated by optimization problems of th e fourth order control system.