Синтез квазиоптимальных законов управления на основе принципа декомпозиции и редукции задачи Лагранжа к изопериметрической в условиях неопределенности

Abstract

The decomposition principle serves as the basis for methods for constructing universal laws of control of mechanical systems that ensure the stability of any target movement from a set of permissible ones and do not contain information about the dynamic parameters of the control object. It is known that the use of reduction of the Lagrange problem to an isoperimetric one makes it possible to obtain an effective solution to the problem of synthesis of nonlinear control laws, the structure of which determines the variant of nonlinear correction of the control laws of the decomposition principle, which provides an increase in performance. This happens due to the fact that the solution of the game problem is obtained under the assumption of the worst variant of disturbing forces. With a known structure of the controlled system or the availability of information about external forces based on their measurement, the correction of the control law makes it possible to improve the quality of control in comparison with the traditional solution. The purpose of this work is to increase the efficiency of control of nonlinear dynamic systems under uncertainty conditions based on the use of a quasi-optimal control structure obtained on the basis of the maximum condition of the generalized power function and the principle of release, and to analyze the effectiveness of the resulting solution in terms of speed using numerical simulation.