On the Synthesis Problem for Optimal Control Systems

Abstract

A new approach to the synthesis problem of optimal controls of feedback type is considered. Algorithms of operating optimal controllers which are able to calculate values of optimal feedbacks during each particular control process in real time are described. The algorithm of operating the controller of the first type (continuous controller) is based on solving special (defining) equations in real time using the Newton method. For operating the optimal controller of the second type (discrete controller) the dual method of linear programming is used. In control problems for systems under uncertainty, a nonstochastic model is used, around which guaranteed results are obtained. Under incomplete and inexact information, problems of optimal observation and identification are introduced. Algorithms of operating the optimal estimator and identifier which are able to construct estimates of available information required for operating the optimal output controller in real time are described. Results are illustrated by optimization problems of the fourth order control system.