GAME THEORY APPLICATIONS TO GUARANTEE OPTIMIZATION IN DYNAMICAL SYSTEMS WITH CONTROL DELAYS

Abstract

In this paper, a linear dynamical system controlled under the conditions of disturbances and with control delays is considered. The Euclidean norm of a set of the system motion deviations at given instants of time from given targets is minimized. Within the game-theoretical approach the problem of calculating the value of the optimal guaranteed result and constructing a positional (closed-loop) control law that ensures this result is posed. For this problem, a solution procedure based on the recurrent construction of upper convex hulls of auxiliary program functions is elaborated. Results of numerical simulations are given.