Periodically intermittent control for finite-time synchronization of delayed quaternion-valued neural networks

Fixed-Time Pinning Common Synchronization and Adaptive Synchronization for Delayed Quaternion-Valued Neural Networks

This article focuses on the fixed-time pinning common synchronization and adaptive synchronization for quaternion-valued neural networks with time-varying delays. First, to reduce transmission burdens and limit convergence time, a pinning controller which only controls partial nodes directly rather than the entire nodes is proposed based on fixed-time control theory. Then, by Lyapunov function approach and some inequalities techniques, fixed-time common synchronization criterion is established. Second, further to realize the self-regulation function of pinning controller, an adaptive pinning controller which can adjust automatically the control gains is developed, the desired fixed-time adaptive synchronization is achieved for the considered system, and the corresponding criterion is also derived. Finally, the availability of these results is tested by simulation example.

Preassigned-time projective synchronization of delayed fully quaternion-valued discontinuous neural networks with parameter uncertainties

This paper concerns with the preassigned-time projective synchronization issue for delayed fully quaternion-valued discontinuous neural networks involving parameter uncertainties through the non-separation method. Above all, based on the existing works, a new preassigned-time stability theorem is established. Subsequently, to realize the control goals, two types of novel and simple chattering-free quaternion controllers are designed, one without the power-law term and the other with a hyperbolic-tangent function. They are different from the existing common power-law controller and exponential controller. Thirdly, under the Filippov discontinuity theories and with the aid of quaternion inequality techniques, some novel succinct sufficient criteria are obtained to ensure the addressed systems to achieve the preassigned-time synchronization by using the preassigned-time stability theory. The preassigned settling time is free from any parameter and any initial value of the system, and can be preset according to the actual task demands. Particularly, unlike the existing results, the proposed control methods can effectively avoid the chattering phenomenon, and the time delay part is removed for simplicity. Additionally, the projection coefficient is generic quaternion-valued instead of real-valued or complex-valued, and some of the previous relevant results are extended. Lastly, numerical simulations are reported to substantiate the effectiveness of the control strategies, the merits of preassigned settling time, and the correctness of the acquired results.

Finite-Time and Fixed-Time Synchronization of Quaternion-Valued Neural Networks With/Without Mixed Delays: An Improved One-Norm Method

In this article, the finite-time synchronization (FTSYN) of a class of quaternion-valued neural networks (QVNNs) with discrete and distributed time delays is studied. Furthermore, the FTSYN and fixed-time synchronization (FIXSYN) of the QVNNs without time delay are investigated. Different from the existing results, which used decomposition techniques, by introducing an improved one-norm, we use a direct analytical method to study the synchronization problems. Incidentally, several properties of one-norm of the quaternion are analyzed, and then, three effective controllers are proposed to synchronize the drive and response QVNNs within a finite time or fixed time. Moreover, efficient criteria are proposed to guarantee that the synchronization of QVNNs with or without mixed time delays can be realized within a finite and fixed time interval, respectively. In addition, the settling times are reckoned. Compared with the existing work, our advantages are mainly reflected in the simpler Lyapunov analytical process and more general activation function. Finally, the validity and practicability of the conclusions are illustrated via four numerical examples.

Exponential Synchronization of Inertial Complex-Valued Fuzzy Cellular Neural Networks with Time-Varying Delays via Periodically Intermittent Control

This paper mainly studies the exponential synchronization issue for the inertial complex-valued fuzzy cellular neural networks (ICVFCNNs) with time-varying delays via periodically intermittent control. To achieve exponential synchronization, we use a non-reduced order and non-separation approach, which is a supplement and innovation to the previous method. Based on directly constructing Lyapunov functional and a novel periodically intermittent control scheme, sufficient conditions for achieving the exponential synchronization of the ICVFCNNs are established. Finally, an example is given to illustrate the validity of the obtained results.