Synchronization of Switched Neural Networks via Attacked Mode-Dependent Event-Triggered Control and Its Application in Image Encryption.

It is challenging to synchronize switched time-delay systems when some modes are uncontrolled and the dwell time (DT) of controlled mode is very small. Therefore, in this article, global exponential synchronization almost surely (GES a.s.) in a cluster of switched neural networks (NNs) with hybrid delays (time-varying delay and infinite-time distributed delay) is investigated, where transition probability (TP)-based random mode-dependent average DT (MDADT) switching is considered. A novel mode-dependent pinning event-triggered controller with nonidentical deception attacks is proposed to save the communication resource and derive less conservative results. The two necessary and restrictive conditions in existing papers that the value of the Lyapunov-Krasovskii functional (LKF) before switching instants should be smaller than that after corresponding instant and the DT of each switching mode is restricted by the sampling intervals of the event trigger are moved. Sufficient conditions in terms of linear matrix inequalities (LMIs) are given to guarantee the GES a.s., even though both synchronizing and nonsynchronizing modes coexist and maybe the minimum DT of synchronizing modes is very small. Numerical examples, including image encryption, are provided to demonstrate the merits of the new technique.

Finite-Time Synchronization of Markovian Coupled Neural Networks With Delays via Intermittent Quantized Control: Linear Programming Approach.

This article is devoted to investigating finite-time synchronization (FTS) for coupled neural networks (CNNs) with time-varying delays and Markovian jumping topologies by using an intermittent quantized controller. Due to the intermittent property, it is very hard to surmount the effects of time delays and ascertain the settling time. A new lemma with novel finite-time stability inequality is developed first. Then, by constructing a new Lyapunov functional and utilizing linear programming (LP) method, several sufficient conditions are obtained to assure that the Markovian CNNs achieve synchronization with an isolated node in a settling time that relies on the initial values of considered systems, the width of control and rest intervals, and the time delays. The control gains are designed by solving the LP. Moreover, an optimal algorithm is given to enhance the accuracy in estimating the settling time. Finally, a numerical example is provided to show the merits and correctness of the theoretical analysis.

Centralized and Collective Neurodynamic Optimization Approaches for Sparse Signal Reconstruction via L1-Minimization.

This article develops several centralized and collective neurodynamic approaches for sparse signal reconstruction by solving the L1 -minimization problem. First, two centralized neurodynamic approaches are designed based on the augmented Lagrange method and the Lagrange method with derivative feedback and projection operator. Then, the optimality and global convergence of them are derived. In addition, considering that the collective neurodynamic approaches have the function of information protection and distributed information processing, first, under mild conditions, we transform the L1 -minimization problem into two network optimization problems. Later, two collective neurodynamic approaches based on the above centralized neurodynamic approaches and multiagent consensus theory are proposed to address the obtained network optimization problems. As far as we know, this is the first attempt to use the collective neurodynamic approaches to deal with the L1 -minimization problem in a distributed manner. Finally, several comparative experiments on sparse signal and image reconstruction demonstrate that our proposed centralized and collective neurodynamic approaches are efficient and effective.

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.

Smoothing inertial neurodynamic approach for sparse signal reconstruction via Lp-norm minimization.

In this paper, we propose a smoothing inertial neurodynamic approach (SINA) which is used to deal with Lp-norm minimization problem to reconstruct sparse signals. Note that the considered optimization problem is nonsmooth, nonconvex and non-Lipschitz. First, the problem is transformed into a smooth optimization problem based on smoothing approximation method, and the Lipschitz property of gradient of the smooth objective function is discussed. Then, SINA based on Karush-Kuhn-Tucker (KKT) condition, smoothing approximation and inertial dynamical approach, is designed to handle smooth optimization problem. The existence, uniqueness, global convergence and optimality of the solution of the SINA are discussed by the Cauchy-Lipschitz-Picard theorem, energy function and KKT condition. In addition, for p=1, the SINA has a mean sublinear convergence rate O1∕t under some mild conditions. Finally, some numerical examples on sparse signal reconstruction and image restoration are given to illustrate the theoretical results and the efficiency of SINA.

Exponential synchronization of semi-Markovian coupled neural networks with mixed delays via tracker information and quantized output controller.

In this paper, exponential synchronization of semi-Markovian coupled neural networks (NNs) with bounded time-varying delay and infinite-time distributed delay (mixed delays) is investigated. Since semi-Markov switching occurs by time-varying probability, it is difficult to capture its precise switching signal. To overcome this difficulty, a tracker is used to track the switching information with some accuracy. Then a quantized output controller (QOC) is designed by using the tracked information. Novel Lyapunov-Krasovskii functionals (LKFs) with negative terms and delay-partitioning approach, which reduce the conservativeness of the obtained results, are utilized to obtain LMI conditions ensuring the exponential synchronization. Moreover, an algorithm is proposed to design the control gains. Our results include both those derived by mode-dependent and mode-independent control schemes as special cases. Finally, numerical simulations validate the effectiveness of the methodology.

Finite-time cluster synchronization for a class of fuzzy cellular neural networks via non-chattering quantized controllers.

This paper considers the finite-time cluster synchronization (FTCS) of coupled fuzzy cellular neural networks (FCNNs) with Markovian switching topology, discontinuous activation functions, proportional leakage, and time-varying unbounded delays. Novel quantized controllers without the sign function are designed to avoid the chattering and save communication resources. Under the framework of Filippov solution, several sufficient conditions are derived to guarantee the FTCS by constructing new Lyapunov-Krasovskii functionals and utilizing M-matrix methods. The new analytical techniques skillfully overcome the difficulties caused by time-varying delays and cope with the uncertainties of both Filippov solution and Markov jumping, which enable us determine the settling time explicitly. Numerical simulations demonstrate the effectiveness of the theoretical analysis.