OPTIMAL PARAMETRIC SYNTHESIS OF STOCHASTIC END POSITION CONTROL SYSTEMS

Abstract

The subject of research in the article is linear stochastic dynamic control systems for the final position. The goal of the work is to synthesize efficient numerical algorithms for machine design of linear stochastic dynamic systems for controlling the final position. The objectives of the study are to build synthesis algorithms based on the application of the method of inversion-conjugate systems, as well as to reduce the dimension of the space of optimized parameters. Applied methods: inversion-conjugate systems for the formation of a quality criterion, methods for reducing the dimension of the space of optimized parameters based on the spectral analysis of the curvature matrix. The obtained results: the search for optimal parameters in the proposed sub-space can be carried out by all methods of the first or second order using the designed matrices. When the minimum point of the criterion is reached in the subspace, the gradient and curvature are calculated in it and, base d on the spectral analysis, a new subspace of the proposed type is constructed, followed by repetition of the optimization process. The proposed search strategy reduces the number of optimization steps. The practical significance of the work lies in the fact that using matrices of conjugate variables, effective methods for calculating the gradient and curvature of the optimization criterion are obtained. Since the time for calculating the gradient according to the proposed dependencies is mainly determin ed by the time of integrating the equations for conjugate matrices, it is approximately equal to the time of integrating the equations for determining the fundamental matrix and variance.