Finite-Time and Fixed-Time Synchronization of Delayed Memristive Neural Networks via Adaptive Aperiodically Intermittent Adjustment Strategy

Adaptive Drive-Response Synchronization of Timescale-Type Neural Networks With Unbounded Time-Varying Delays

In recent years, adaptive drive-response synchronization (DRS) of two continuous-time delayed neural networks (NNs) has been investigated extensively. For two timescale-type NNs (TNNs), how to develop adaptive synchronization control schemes and demonstrate rigorously is still an open problem. This article concentrates on adaptive control design for synchronization of TNNs with unbounded time-varying delays. First, timescale-type Barbalat lemma and novel timescale-type inequality techniques are first proposed, which provides us practical methods to investigate timescale-type nonlinear systems. Second, using timescale-type calculus, novel timescale-type inequality, and timescale-type Barbalat lemma, we demonstrate that global asymptotic synchronization can be achieved via adaptive control under algebraic and matrix inequality criteria even if the time-varying delays are unbounded and nondifferentiable. Adaptive DRS is discussed for TNNs, which implies our control schemes are suitable for continuous-time NNs, their discrete-time counterparts, and any combination of them. Finally, numerical examples on TNNs and timescale-type chaotic Ikeda-like oscillator with unbounded time-varying delays are carried out to verify the adaptive control schemes.

Adaptive control for memristive system via compensatory controller and Chebyshev neural network

In this paper, based on linear matrix inequality technique, a simple controller and a compensatory controller are designed. It can track arbitrary fixed points and any periodic orbits. In addition, a synchronization control method via Chebyshev neural network with external disturbances is proposed. An adaptive controller is given. The Chebyshev neural network is used to approximate the uncertain nonlinear function and the adaptive law is used to adjust the corresponding parameters in the system. Taking a 4D memristive chaotic system as examples, the results are in consistent with the simulations. From a framework and control theoretical point of view, the proposed synchronization approach via compensation controller and Chebyshev neural network is firstly presented. From an application point of view, the proposed scheme can simplify the complexity of controller design. It is promising in many applications for mem-systems as secure communications and neural networks.

Synchronization of inertial complex-valued memristor-based neural networks with time-varying delays

The synchronization of inertial complex-valued memristor-based neural networks (ICVMNNs) with time-varying delays was explored in the paper with the non-separation and non-reduced approach. Sufficient conditions required for the exponential synchronization of the ICVMNNs were identified with the construction of comprehensive Lyapunov functions and the design of a novel control scheme. The adaptive synchronization was also investigated based on the derived results, which is easier to implement in practice. What's more, a numerical example that verifies the obtained results was presented.

Projective Synchronization of Delayed Uncertain Coupled Memristive Neural Networks and Their Application

In this article, the authors analyzed the nonlinear effects of projective synchronization between coupled memristive neural networks (MNNs) and their applications. Since the complete signal transmission is difficult under parameter mismatch and different projective factors, the delays, which are time-varying, and uncertainties have been taken to realize the projective synchronization of MNNs with multi-links under the nonlinear control method. Through the extended comparison principle and a new approach to dealing with the mismatched parameters, sufficient criteria have been determined under different types of projective factors and the framework of the Lyapunov-Krasovskii functional (LKF) for projective convergence of the coupled MNNs. Instead of the classical treatment for secure communication, the concept of error of synchronization between the drive and response systems has been applied to solve the signal encryption/decryption problem. Finally, the simulations in numerical form have been demonstrated graphically to confirm the adaptability of the theoretical results.

Fixed-time projective synchronization of delayed memristive neural networks via aperiodically semi-intermittent switching control

This paper studies the fixed-time projective synchronization problem for a class of delayed memristive neural networks via aperiodically semi-intermittent switching control. Instead of using the common traditional controller containing two power exponent terms, a novel aperiodically semi-intermittent switching controller is designed, containing only one power exponent term which serves as a function of the state of the error system. With the aid of the extended differential inclusion framework, the analysis method, and the inequality technique, some new sufficient conditions are derived to guarantee fixed-time projective synchronization for the considered systems. Compared with periodically semi-intermittent control methods, the control time width of each section in aperiodically semi-intermittent control can be adjusted. Especially, the settling time is directly reckoned, which is closely related to the number of neurons and the maximum ratio of the second subinterval span in each non-periodic span to all non-periodic time spans rather than the initial value. Additionally, the projection synchronization has a strong practicality, as the projection coefficient can be adjusted for different needs instead of being fixed. Meanwhile, the study improves some previous related works. Ultimately, a numerical example is given to substantiate the correctness of the obtained results.