Prescribed-Time Synchronization of Coupled Memristive Neural Networks with Heterogeneous Impulsive Effects

Effects of impulse on prescribed-time synchronization of switching complex networks

The specified convergence time, designated by the user, is highly attractive for many high-demand applications such as industrial robot control, missile guidance, and autonomous vehicles. For the application of neural networks in the field of secure communication and power systems, the importance of prescribed-time synchronization(PTs) and stable performance of the system is more prominent. This paper introduces a prescribed-time controller without the fractional power function and sign function, which can reach synchronization at a prescribed time and greatly reduce the chattering phenomenon of neural networks. Additionally, by constructing synchronizing/desynchronizing impulse sequences, the PTs of switching complex networks(SCN) is achieved with impulse effects, where the time sequences of switching and impulse occurrences in the networks are constrained by the average dwell time. This approach effectively reduces the impact of frequent mode switching on network synchronization, and the synchronization time can be flexibly adjusted within any physically allowable range to accommodate different application requirements. Finally, the effectiveness of the proposed control strategy is demonstrated by two examples.

Resilient fixed-time stabilization of switched neural networks subjected to impulsive deception attacks

This article focuses on the resilient fixed-time stabilization of switched neural networks (SNNs) under impulsive deception attacks. A novel theorem for the fixed-time stability of impulsive systems is established by virtue of the comparison principle. Existing fixed-time stability theorems for impulsive systems assume that the impulsive strength is not greater than 1, while the proposed theorem removes this assumption. SNNs subjected to impulsive deception attacks are modeled as impulsive systems. Some sufficient criteria are derived to ensure the stabilization of SNNs in fixed time. The estimation of the upper bound for the settling time is also given. The influence of impulsive attacks on the convergence time is discussed. A numerical example and an application to Chua's circuit system are given to demonstrate the effectiveness of the theoretical results.

Fixed/prescribed-time synchronization of BAM memristive neural networks with time-varying delays via convex analysis

The synchronization problem of bidirectional associative memory memristive neural networks (BAMMNNs) with time-varying delays plays an essential role in the implementation and application of neural networks. Firstly, under the framework of the Filippov's solution, the discontinuous parameters of the state-dependent switching are transformed by convex analysis method, which is different from most previous approaches. Secondly, based on Lyapunov function and some inequality techniques, several conditions for the fixed-time synchronization (FXTS) of the drive-response systems are obtained by designing special control strategies. Moreover, the settling time (ST) is estimated by the improved fixed-time stability lemma. Thirdly, the driven-response BAMMNNs are investigated to be synchronized within a prescribed time by designing new controllers based on the FXTS results, where ST is irrelevant to the initial values of BAMMNNs and the parameters of controllers. Finally, a numerical simulation is exhibited to verify the correctness of the conclusions.

Predefined-time synchronization of coupled neural networks with switching parameters and disturbed by Brownian motion

This article focuses on predefined time synchronization problem for a class of signal switching neural networks with time-varying delays. In the network models, we not only consider the coupling characteristics in the following networks, but also consider the disturbance with standard Brownian motion. In the design of the controller, the control gain is designed as 1ɛ+T_p-t (t∈[T₀,T_p), ɛ is an optional smaller positive number), which avoids the infinite gain (the control gain is designed as 1T_p-t in other reference). In order to get the predefined time control law, a power function is multiplied to the Lyapunov functional, from which it can get an exponential upper bound function via the derivative and mathematical expectation operation. Utilizing the martingale theory and the method of Laplace matrix, some novel predefined time synchronization criteria are obtained for the leader-following neural networks, meanwhile the following networks can maintain the leader network after achieved synchronization. Based on the special network of the main system, five corollaries separately develop the predefined time synchronization results from different perspectives. An example with some simulation figures and computing results fully exhibits the effectiveness of the achieved synchronization scheme. In this case, although the error signal is disturbed by Brownian motion, the trace signal can still stably converge to zero by this control scheme, meanwhile the predefined-time control effect is achieved.

Predefined-Time Stability/Synchronization of Coupled Memristive Neural Networks With Multi-Links and Application in Secure Communication

This paper explores the realization of a predefined-time synchronization problem for coupled memristive neural networks with multi-links (MCMNN) via nonlinear control. Several effective conditions are obtained to achieve the predefined-time synchronization of MCMNN based on the controller and Lyapunov function. Moreover, the settling time can be tunable based on a parameter designed by the controller, which is more flexible than fixed-time synchronization. Then based on the predefined-time stability criterion and the tunable settling time, we propose a secure communication scheme. This scheme can determine security of communication in the aspect of encrypting the plaintext signal with the participation of multi-links topology and coupled form. Meanwhile, the plaintext signals can be recovered well according to the given new predefined-time stability theorem. Finally, numerical simulations are given to verify the effectiveness of the obtained theoretical results and the feasibility of the secure communication scheme.