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

A method for the quasi-optimal synthesis of a multi-mode synchronization system based on the maximum condition of the generalized power function has been developed. The effectiveness of its operation in capture mode is demonstrated on the basis of mathematical modeling. The results showed high resistance to disturbances and a decrease in the synchronization error of the multimode system in the steady state.

Keywords: phase locked loop, combined maximum principle, multi-mode control

A method for the intellectualization of measurement procedures has been developed. It is based on the step-by-step optimization procedure, which provides a reduction of the stochastic estimation problem to a number of deterministic problems. The task of the first stage of optimization is the synthesis of an adaptive mathematical model of the measuring process based on the combined principle of maximum, which, unlike the known methods, will ensure the constructiveness of its use in the next stages of optimization. The task of the subsequent stages of optimization is to solve the estimation problem based on the regularization method A.N. Tikhonov. Equations of an iterative measurement procedure are obtained that differ from the state transition vector functions known in structure. It belongs to the category of intelligent measuring procedures, since it makes a targeted choice of the closest to the true value of the assessment of the measured parameter in the conditions of structural uncertainty of the model of the studied object and parametric uncertainty of the observation model.

Keywords: two-stage synthesis, intellectualization, the combined principle of maximum, regularization

Dynamic synthesis filter problem is presented in the form of the optimal control problem. The solution is obtained based on theorem of the maximum function of the generalized forces and the transformation equations of motion based on a characteristic of the Lagrangian analysis of the trajectories in the phase space-stve. It allows you to build Quasideterministic-ing model managed movement which admits repents representation as a quasi-linear. Syn-thesis Unity equation of the optimal filter dy-namic motion estimation parameters differs from the known feedback design. Abstract transient and stable operation is designed filter. Comparisons conducted with the results that are obtained using adaptive algorithm for esti-mating the moving Kaufman and alpha-β filter. On the basis of mathematical modeling showed that the evaluation of the filter have a higher accuracy at a lower cost computing.

Keywords: kinetic potential, optimal filter, the combined maximum principle.

Universal method of optimal control synthesis offers a versatile method for the synthesis of optimal controls provides a solution to the synthesis problem for the class of piecewise constant functions for Lagrangian dynamical systems, the shape of the control law depends only on the structure of the cost functional and does not depend on the structure of the existing system of generalized forces. The effectiveness of the method is confirmed by a minimum of computational costs, as well as the maximum rate of convergence and accuracy to achieve the desired trajectory in comparison with the known solution for example has become a test for testing various control methods for the synthesis problem of a simple pendulum.

Keywords: combined maximum principle, optimal control, mathematical pendulum