Synthesis of phase-locked frequency systems under perturbation conditions based on the model of the combined maximum principle and the discrete method of invariant immersion

Abstract

Synthesis of phase-locked frequency systems under perturbation conditions based on the model of the combined maximum principle and the discrete method of invariant immersion

Kostoglotov A.A., Lazarenko S.V., Pugachev I.V.

Incoming article date: 25.11.2020

The synthesis of phase-locked frequency systems is based on a two-stage optimization procedure. This makes it possible to apply the combined maximum principle to construct a model of the signal phase dynamics under conditions of structural uncertainty of regular effects. The estimation equations in the form of a two-point boundary value problem are obtained using the discrete maximum principle Of L. S. Pontryagin, and a recurrent estimation algorithm is obtained using the invariant immersion method. The efficiency of the synthesized phase-locked frequency system was evaluated on the basis of mathematical modeling in comparison with the traditional one by the criteria of convergence rate and accuracy.

Keywords: synthesis, phase auto-tuning of frequency, the maximum principle of L. S. Pontryagin, the maximum condition of the generalized power function