The theory of hidden oscillations, developed by N.V. Kuznetsov, RAS Corresponding Member, and his scientific school, was stated as one of the most important results of the past year mentioned by G.Ya. Krasnikov, Academician, the President of the Russian Academy of Sciences, in the report On the Most Important Scientific Achievements Obtained by Russian Scientists in 2022 at the General Meeting of RAS Members on May 23, 2023.

The methods of the theory of hidden oscillations were created and developed, that allowed to advance in solving a number of well-known fundamental problems and proved to be widely in demand for topical applied researches. In practice, the transition of the control system state to a hidden attractor, which was caused by external disturbances, leads to undesirable operating modes and is often the cause of accidents and man-made disasters. The theory of hidden oscillations opened up fundamentally new possibilities for determining the boundaries of stability and identifying undesirable oscillations to prevent technological and man-made disasters. Detected were hidden oscillations in nonlinear control systems and counterexamples to the problem of R.E. Kalman, in the closed model for control of the Sayano-Shushenskaya HPP hydraulic unit, in models of drilling rigs, in nonlinear models for flutter suppression (the problem of M.V. Keldysh), in the L. Chua generator, etc. Since 2019, the results obtained have been applied jointly with industrial companies to solve a number of urgent practical problems, including those which arise when designing power supply systems for railway rolling stock, promising electrified aircraft and models of MEMS gyroscopes.

For his work on the Theory of hidden oscillations and stability of dynamical systems N.V. Kuznetsov became a laureate of the St. Petersburg State University Prize in 2020 for scientific works and in 2021 he received the International Prize named after V. Afraimovich (Afraimovich Award).

1. Kuznetsov N.V., Mokaev T. N., Ponomarenko V. I., Seleznev E. P., Stankevich N. V., Chua L. (2023). Hidden attractors in Chua circuit: mathematical theory meets physical experiments Hidden attractors in Chua circuit: mathematical theory meets physical experiments. Nonlinear Dynamics. 111 (6): 5859–58872. N.V. Kuznetsov, B. Andrievsky, E.V. Kudryashova, O.A. Kuznetsova, Stability and hidden oscillations analysis of the spacecraft attitude control system using reaction wheels, Aerospace Science and Technology, 131, 2022, 107973
3. N.V. Kuznetsov, Y.V. Belyaev, A.V. Styazhkina, M.V. Yuldashev, R.V. Yuldashev, Effects of PLL Architecture on MEMS Gyroscope Performance, Gyroscopy and Navigation, 13(1), 2022, 44-52
4. I.M. Boiko, N.V. Kuznetsov, R.N. Mokaev, T.N. Mokev, M.V. Yuldashev, R.V. Yuldashev, On counter-examples to Aizerman and Kalman conjectures, International Journal of Control, 95(4), 2022, 906-913