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New fixed‐time synchronization control of discontinuous inertial neural networks via indefinite Lyapunov‐Krasovskii functional method
Author(s) -
Kong Fanchao,
Zhu Quanxin
Publication year - 2020
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.5297
Subject(s) - correctness , inertial frame of reference , classification of discontinuities , mathematics , control theory (sociology) , synchronization (alternating current) , differential inclusion , artificial neural network , settling time , transformation (genetics) , lyapunov function , set (abstract data type) , control (management) , computer science , mathematical analysis , topology (electrical circuits) , nonlinear system , algorithm , artificial intelligence , chemistry , engineering , biochemistry , quantum mechanics , machine learning , step response , programming language , physics , combinatorics , control engineering , gene
Summary The purpose of this article is to investigate the existence of periodic solutions and fixed‐time synchronization (FTS) of a class of discontinuous inertial neural networks (DINNs) with time‐varying delays. Due to the existence of the discontinuities, first, by using a generalized variable transformation, the original DINNs are transformed into a first‐order differential system. By using the differential inclusions theory and the set‐valued version of the Mawhin coincidence theorem, a new delay‐dependent criterion is derived to ensure the existence of periodic solutions. Furthermore, by designing some effective discontinuous control strategies and by constructing indefinite Lyapunov‐Krasovskii functional (LKF), algebraic criteria are derived to guarantee the FTS for the drive‐response system. The settling time is explicitly estimated. In comparison with the related results on INNs, it is the first time to study the existence result of the DINNs and the Lyapunov approaches applied to investigate the FTS are entirely different. Finally, the correctness of the main results is verified via numerical examples.