Affiliation:
1. School of Computer Science, Huainan Normal University, Huainan 232038, China
2. School of Finance and Mathematics, Huainan Normal University, Huainan 232038, China
Abstract
Asymptotic synchronization requires continuous external control of the system, which is unrealistic considering the cost of control. Adaptive control methods have strong robustness to uncertainties such as disturbances and unknowns. On the other hand, for finite-time synchronization, if the initial value of the system is unknown, the synchronization time of the finite-time synchronization cannot be estimated. This paper explores the finite-time adaptive synchronization (FTAS) and fixed-time synchronization (FDTS) of fractional-order memristive cellular neural networks (FMCNNs) with time-varying delays (TVD). Utilizing the properties and principles of fractional order, we introduce a novel lemma. Based on this lemma and various analysis techniques, we establish new criteria to guarantee FTAS and FDTS of FMCNNs with TVD through the implementation of a delay-dependent feedback controller and fractional-order adaptive controller. Additionally, we estimate the upper bound of the synchronization setting time. Finally, numerical simulations are conducted to confirm the validity of the finite-time and fixed-time stability theorems.
Funder
The Natural Science Foundation of Anhui Province
The Program for Innovative Research Team in Universities of Anhui Province
The University Natural Science Foundation of Anhui Province
National Natural Science Foundation of China
The Research and Development Plan Project Foundation of Huainan