Yu.P. Kornyushin – Dr.Sc.(Eng.), Professor, 
Department «Automatic Control Systems and Electrical Engineering», Kaluga branch of the Bauman MSTU E-mail: theroland@yandex.ru
P.Yu. Kornyushin – Post-graduate Student, 
Department «Automatic Control Systems and Electrical Engineering», Kaluga branch of the Bauman MSTU E-mail: kornyushin.petr@gmail.com
I.K. Ustinov – Ph.D.(Eng.), Associate Professor, 
Department «Mechanical Engineering Technologies», Kaluga branch of the Bauman MSTU E-mail: ustiovigorkir@yandex.ru

The problem of synthesis of optimal control (regulators), which provides tracking of the phase coordinates of a nonlinear control object for an arbitrarily changing signal, is considered.
To develop a synthesis method for physically realizable regulators for servo systems for a class of nonlinear control objects that form control based on the feedback principle.
A new synthesis algorithm is proposed, which includes: 1) Linearization of nonlinear equations describing the dynamics of the control object according to the Newton – Kantorovich scheme; 2) Construction of programmed control of the object and reduction of the two-point boundary value problem to the Cauchy problem using matrix operators; 3) Formation of an algorithm for the functioning of the regulator of the tracking system («defrosting» the initial state of the control object and organizing the iterative process).
The proposed algorithm can be used in the design of effective systems that automatically track the frequency and phase of input oscillations in radio receivers, systems for automatic tracking of the temporal position of radio and video pulses in radar, radio navigation, radio control, sighting systems, goniometric tracking systems, designed for tracking targets, tracking behind artificial earth satellites or other objects of near space, etc.

Kornyushin Yu.P., Kornyushin P.Yu., Ustinov I.K. Synthesis of optimal regulators of servo systems based on reduction of the two-point problem to the Cauchy problem. Electromagnetic waves and electronic systems. 2020. V. 25. № 4. P. 56−65. DOI: 10.18127/j15604128-202004-07. (in Russian)

1. Krasovskii N.N. Teoriya upravleniya dvizheniem. Lineinye sistemy. M.: Nauka. 1968. 476 s. (in Russian)
2. Boltyanskii V.G. Matematicheskie metody optimalnogo upravleniya. M.: Nauka. 1969. 408 s. (in Russian)
3. Braison A., Kho Yu-Shi. Prikladnaya teoriya optimalnogo upravleniya. M.: Mir. 1972. 544 s. (in Russian)
4. Aleksandrov V.V., Boltyanskii V.G., Lemak S.S., Parusnikov N.A., Tikhomirov V.M. Optimalnoe upravlenie dvizheniem. M.: FIZMATLIT. 2005. 376 s. (in Russian)
5. Kornyushin Yu.P. Sintez regulyatorov nelineinykh sledyashchikh radiotekhnicheskikh sistem. Elektromagnitnye volny i elektronnye sistemy. 2019. № 6. S. 59−63. DOI: 10.18127/j15604128-201906-08. (in Russian)
6. Kornyushin Yu.P. Primenenie metodov nelineinogo programmirovaniya i matrichnykh operatorov v zadache sinteza regulyatorov sledyashchikh sistem. Elektromagnitnye volny i elektronnye sistemy. 2019. № 6. S. 64−70. DOI: 10.18127/j15604128-201906-09. (in Russian)
7. Gaiskii V.A., Egupov N.D., Kornyushin Yu.P. Primenenie funktsii Uolsha v sistemakh avtomatizatsii nauchnykh issledovanii. Kiev: Naukova dumka. 1993. 212 s. (in Russian)
8. Kornyushin Yu.P., Melnikov D.V., Egupov N.D., Kornyushin P.Yu. Sintez dopolnitelnogo regulyatora dlya stabilizatsii uglovoi skorosti rotora parovoi turbiny. Vestnik MGTU im. N.E. Baumana. Ser. Estestvennye nauki. 2015. № 5(62). S. 100−112. (in Russian)
9. Kornyushin Yu.P., Egupov N.D., Kornyushin P.Yu. Identifikatsiya nelineinykh ob'ektov i sistem upravleniya s ispolzovaniem apparata matrichnykh operatorov. Inzhenernyi zhurnal: nauka i innovatsii. 2014. № 6.URL: http://engjournal.ru/catalog/appmath/hidden/1315.html (data obrashcheniya: 12.07.2020). (in Russian)