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

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