Construction of the domain of attraction based on Lyapunov functions for general nonlinear systems
https://doi.org/10.37493/2307-910X.2022.3.1
Abstract
The paper proposes an algorithm for constructing Lyapunov candidate neural network functions in order to maximize the estimate of the area of attraction of the equilibrium position. To do this, it is necessary that the invariant subset, given by the level set, occupy the largest possible share of the empirical estimate of the attraction region obtained by the simulation. The implementation of this goal is carried out by introducing an additional term in the loss function. The algorithm makes it possible to construct candidate functions for systems with non-linearities of a rather general form. The operation of the algorithm is illustrated by an example.
About the Authors
S. A. Romanov
Saint Petersburg Electrotechnical University "LETI”
Russian Federation
Russian Federation
Sergey A. Romanov - Researcher at the Department of Automation and Control Processes of the St. Petersburg State Electrotechnical University "LETI" named after V.I. Ulyanov (Lenin).
St. Petersburg, Professora Popova str., house 5
S. E. Dushin
Saint Petersburg Electrotechnical University "LETI”
Russian Federation
Russian Federation
Sergey E. Dushin - Doctor of Technical Sciences, Professor of the Department of Automation and Control Processes of the St. Petersburg State Electrotechnical University "LETI" named after V.I. Ulyanov (Lenin).
St. Petersburg, Professora Popova str., house 5
Tel.: +7 (921) 970-46-31
I. I. Shpakovshaya
Saint Petersburg Electrotechnical University "LETI”
Russian Federation
Russian Federation
Irina I. Shpakovskaya - Assistant of the Department of Automation and Control Processes of the St. Petersburg State Electrotechnical University "LETI" named after V.I. Ulyanov (Lenin).
St. Petersburg, Professora Popova str., 5
Tel.: +7 (950) 049-71-40
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Review
For citations:
Romanov S.A., Dushin S.E., Shpakovshaya I.I. Construction of the domain of attraction based on Lyapunov functions for general nonlinear systems. Modern Science and Innovations. 2022;(3):10-19. https://doi.org/10.37493/2307-910X.2022.3.1
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