CONTROLABILITY AND PERFORMANCE OF LINEAR SYSTEMS

Authors

A.A. Bayzakova Al-Farabi Kazakh National University
S.A. Aysagaliev Al-Farabi Kazakh National University

Keywords:

controllability, optimal performance, integral equation, optimal control, minimizing sequences.

Abstract

A new method for solving the problem of controllability and optimal performance of linear systems with a given boundary condition and a constraint on control values is developed, including for cases where the set that determines the constraints on control values depends on time. The difference of the proposed method from the known approaches to the problem of controllability and optimal speed is that by constructing a general solution of the Fredholm integral equation of the first kind with a fixed parameter, the original boundary value problem is reduced to solving the initial problem of optimal control. The solution of the problem of optimal performance can be obtained on the basis of solving the general problem of controllability. Necessary and sufficient conditions for the existence of a solution to the controllability problem and a method for solving it by constructing minimizing sequences are obtained. An estimate for the rate of convergence of minimizing sequences is obtained.

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