An LMI approach for exponential synchronization of switched stochastic competitive neural networks with mixed delays

Saturation function-based continuous control on fixed-time synchronization of competitive neural networks

Currently, through proposing discontinuous control strategies with the signum function and discussing separately short-term memory (STM) and long-term memory (LTM) of competitive artificial neural networks (ANNs), the fixed-time (FXT) synchronization of competitive ANNs has been explored. Note that the method of separate analysis usually leads to complicated theoretical derivation and synchronization conditions, and the signum function inevitably causes the chattering to reduce the performance of the control schemes. To try to solve these challenging problems, the FXT synchronization issue is concerned in this paper for competitive ANNs by establishing a theorem of FXT stability with switching type and developing continuous control schemes based on a kind of saturation functions. Firstly, different from the traditional method of studying separately STM and LTM of competitive ANNs, the models of STM and LTM are compressed into a high-dimensional system so as to reduce the complexity of theoretical analysis. Additionally, as an important theoretical preliminary, a FXT stability theorem with switching differential conditions is established and some high-precision estimates for the convergence time are explicitly presented by means of several special functions. To achieve FXT synchronization of the addressed competitive ANNs, a type of continuous pure power-law control scheme is developed via introducing the saturation function instead of the signum function, and some synchronization criteria are further derived by the established FXT stability theorem. These theoretical results are further illustrated lastly via a numerical example and are applied to image encryption.

Fixed-Time Synchronization of Competitive Neural Networks With Multiple Time Scales

In this brief, we investigate the fixed-time synchronization of competitive neural networks with multiple time scales. These neural networks play an important role in visual processing, pattern recognition, neural computing, and so on. Our main contribution is the design of a novel synchronizing controller, which does not depend on the ratio between the fast and slow time scales. This feature makes the controller easy to implement since it is designed through well-posed algebraic conditions (i.e., even when the ratio between the time scales goes to 0, the controller gain is well defined and does not go to infinity). Last but not least, the closed-loop dynamics is characterized by a high convergence speed with a settling time which is upper bounded, and the bound is independent of the initial conditions. A numerical simulation illustrates our results and emphasizes their effectiveness.

Fixed-time synchronization of discontinuous competitive neural networks with time-varying delays

In this article, the fixed-time (FXT) synchronization of discontinuous competitive neural networks (CNNs) involving time-varying delays is investigated. Firstly, two kinds of discontinuous FXT control schemes are proposed and two forms of Lyapunov function are constructed based on p-norm and 1-norm to discuss the FXT synchronization of CNNs. By means of nonsmooth analysis and some inequality techniques, some simple criteria are obtained to achieve FXT synchronization and the upper bound of the settling time with less conservativeness is provided. Furthermore, the effect of time scale on FXT synchronization of CNNs is considered. Lastly, some numerical results for an example are provided to demonstrate the derived theoretical results.

Finite-time bipartite synchronization of switched competitive neural networks with time delay via quantized control

This article tackles the finite-time bipartite synchronization (FTBS) of coupled competitive neural networks (CNNs) with switching parameters and time delay. Quantized control is utilized to achieve the FTBS at a small control cost and with limited channel resources. Since the effects of the time delay and switching parameters, traditional finite-time techniques cannot be directly utilized to the FTBS. By constructing a novel multiple Lyapunov functional (MLF), a sufficient criterion formulated by linear programming (LP) is established for the FTBS and the estimation of the settling time. To further improve the accuracy of the settling time, another MLF is designed by dividing the dwell time. With the aid of convex combination, a new LP is provided, which removes the requirement that the increment coefficient of the MLF at switching instants has to be larger than 1. In addition, to obtain the more precise settling time, an optimal algorithm is provided. Two numerical examples are put forward to demonstrate the reasonableness of the theoretical analysis.

Predefined-time synchronization of competitive neural networks

In this paper, the predefined-time synchronization of competitive neural networks (CNNs) is researched based on two different predefined-time stability theorems. In view of the bilayer structure of CNNs, we design two bilayer predefined-time controllers. The first controller utilizes sign function, while the second controller utilizes exponential function and Lyapunov function. In these two controllers, the predefined time is set as a controller parameter, and it can be an arbitrary positive constant. Under these two controllers, the considered CNNs can achieve synchronization within the predefined time regardless of the initial values. A specific example is presented to validate the theoretical results.