Finite-Time Synchronization and H∞ Synchronization for Coupled Neural Networks With Multistate or Multiderivative Couplings

This article investigates the finite-time synchronization (FTS) and H∞ synchronization for two types of coupled neural networks (CNNs), that is, the cases with multistate couplings and with multiderivative couplings. By designing appropriate state feedback controllers and parameter adjustment strategies, some FTS and finite-time H∞ synchronization criteria for CNNs with multistate couplings are derived. In addition, we further consider the FTS and finite-time H∞ synchronization problems for CNNs with multiderivative couplings by utilizing state feedback control approach and selecting suitable parameter adjustment schemes. Finally, two simulation examples are given to demonstrate the effectiveness of the proposed criteria.

Intralayer Synchronization of Multiplex Dynamical Networks via Pinning Impulsive Control

These days, the synchronization of multiplex networks is an emerging and important research topic. Grounded framework and theory about synchronization and control on multiplex networks are yet to come. This article studies the intralayer synchronization on a multiplex network (i.e., a set of networks connected through interlayer edges), via the pinning impulsive control method. The topologies of different layers are independent of each other, and the individual dynamics of nodes in different layers are different as well. Supra-Laplacian matrices are adopted to represent the topological structures of multiplex networks. Two cases are considered according to impulsive sequences of multiplex networks: 1) pinning controllers are applied to all the layers simultaneously at the instants of a common impulse sequence and 2) pinning controllers are applied to each layer at the instants of distinct impulse sequences. Using the Lyapunov stability theory and the impulsive control theory, several intralayer synchronization criteria for multiplex networks are obtained, in terms of the supra-Laplacian matrix of network topology, self-dynamics of nodes, impulsive intervals, and the pinning control effect. Furthermore, the algorithms for implementing pinning schemes at every impulsive instant are proposed to support the obtained criteria. Finally, numerical examples are presented to demonstrate the effectiveness and correctness of the proposed schemes.

Finite-Horizon Optimal Control of Boolean Control Networks: A Unified Graph-Theoretical Approach

This article investigates the finite-horizon optimal control (FHOC) problem of Boolean control networks (BCNs) from a graph theory perspective. We first formulate two general problems to unify various special cases studied in the literature: 1) the horizon length is a priori fixed and 2) the horizon length is unspecified but finite for given destination states. Notably, both problems can incorporate time-variant costs, which are rarely considered in existing work, and a variety of constraints. The existence of an optimal control sequence is analyzed under mild assumptions. Motivated by BCNs' finite state space and control space, we approach the two general problems intuitively and efficiently under a graph-theoretical framework. A weighted state transition graph and its time-expanded variants are developed, and the equivalence between the FHOC problem and the shortest-path (SP) problem in specific graphs is established rigorously. Two algorithms are developed to find the SP and construct the optimal control sequence for the two problems with reduced computational complexity, though technically, a classical SP algorithm in graph theory is sufficient for all problems. Compared with existing algebraic methods, our graph-theoretical approach can achieve state-of-the-art time efficiency while targeting the most general problems. Furthermore, our approach is the first one capable of solving Problem 2) with time-variant costs. Finally, a genetic network in the bacterium E. coli and a signaling network involved in human leukemia are used to validate the effectiveness of our approach. The results of two common tasks for both networks show that our approach can dramatically reduce the running time. Python implementation of our algorithms is available at GitHub https://github.com/ShuhuaGao/FHOC.

Guaranteed Cost Finite-Time Control of Uncertain Coupled Neural Networks

This article investigates a robust guaranteed cost finite-time control for coupled neural networks with parametric uncertainties. The parameter uncertainties are assumed to be time-varying norm bounded, which appears on the system state and input matrices. The robust guaranteed cost control laws presented in this article include both continuous feedback controllers and intermittent feedback controllers, which were rarely found in the literature. The proposed guaranteed cost finite-time control is designed in terms of a set of linear-matrix inequalities (LMIs) to steer the coupled neural networks to achieve finite-time synchronization with an upper bound of a guaranteed cost function. Furthermore, open-loop optimization problems are formulated to minimize the upper bound of the quadratic cost function and convergence time, it can obtain the optimal guaranteed cost periodically intermittent and continuous feedback control parameters. Finally, the proposed guaranteed cost periodically intermittent and continuous feedback control schemes are verified by simulations.

Global dissipativity and finite-time synchronization of mixed time-varying delayed memristor-based neural networks with discontinuous activations

In this paper, the matters of dissipativity and finite time synchronization for memristor-based neural networks (MNNs) with mixed time-varying discontinuities are investigated. Firstly, under the framework of extending Filippov differential inclusion theory, several effective new criteria are derived. Then, the global dissipativity of Filippov solution to neural networks is proved by using generalized Halanay inequality and matrix measure method. Secondly, some novel sufficient conditions are introduced to guarantee the finite-time synchronization of the drive-response MNNs based on a simple Lyapunov function and two different feedback controllers. Finally, several numerical examples are given to verify the validity of the theoretical results.

Necessary and Sufficient Conditions for Group Consensus of Fractional Multiagent Systems Under Fixed and Switching Topologies via Pinning Control

The group consensus problem for fractional-order multiagent systems is investigated in this paper. With the help of double-tree-form transformations, the group consensus problem of fractional-order multiagent systems is proved to be equivalent to the asymptotical stability problem of reduced-order error systems. A class of distributed control protocols and some simple LMI sufficient conditions as well as necessary and sufficient conditions are proposed in this paper to solve the group consensus problem for fractional multiagent systems. Moreover, pinning control strategy has been taken into consideration. It is shown that the system converges more rapidly when the designed pinning protocols are adopted. In addition, the case of fractional system with switching topologies is also discussed and some corresponding sufficient conditions are obtained. Finally, some simulation results are presented to illustrate the theoretical results.

Stability Analysis of Quaternion-Valued Neural Networks: Decomposition and Direct Approaches

In this paper, we investigate the global stability of quaternion-valued neural networks (QVNNs) with time-varying delays. On one hand, in order to avoid the noncommutativity of quaternion multiplication, the QVNN is decomposed into four real-valued systems based on Hamilton rules: $ij=-ji=k,~jk=-kj=i$ , $ki=-ik=j$ , $i^{2}=j^{2}=k^{2}=ijk=-1$ . With the Lyapunov function method, some criteria are, respectively, presented to ensure the global $\mu $ -stability and power stability of the delayed QVNN. On the other hand, by considering the noncommutativity of quaternion multiplication and time-varying delays, the QVNN is investigated directly by the techniques of the Lyapunov-Krasovskii functional and the linear matrix inequality (LMI) where quaternion self-conjugate matrices and quaternion positive definite matrices are used. Some new sufficient conditions in the form of quaternion-valued LMI are, respectively, established for the global $\mu $ -stability and exponential stability of the considered QVNN. Besides, some assumptions are presented for the two different methods, which can help to choose quaternion-valued activation functions. Finally, two numerical examples are given to show the feasibility and the effectiveness of the main results.

Synchronization Control for a Class of Discrete-Time Dynamical Networks With Packet Dropouts: A Coding-Decoding-Based Approach

The synchronization control problem is investigated for a class of discrete-time dynamical networks with packet dropouts via a coding-decoding-based approach. The data is transmitted through digital communication channels and only the sequence of finite coded signals is sent to the controller. A series of mutually independent Bernoulli distributed random variables is utilized to model the packet dropout phenomenon occurring in the transmissions of coded signals. The purpose of the addressed synchronization control problem is to design a suitable coding-decoding procedure for each node, based on which an efficient decoder-based control protocol is developed to guarantee that the closed-loop network achieves the desired synchronization performance. By applying a modified uniform quantization approach and the Kronecker product technique, criteria for ensuring the detectability of the dynamical network are established by means of the size of the coding alphabet, the coding period and the probability information of packet dropouts. Subsequently, by resorting to the input-to-state stability theory, the desired controller parameter is obtained in terms of the solutions to a certain set of inequality constraints which can be solved effectively via available software packages. Finally, two simulation examples are provided to demonstrate the effectiveness of the obtained results.

Cluster Synchronization for Interacting Clusters of Nonidentical Nodes via Intermittent Pinning Control

The cluster synchronization problem is investigated using intermittent pinning control for the interacting clusters of nonidentical nodes that may represent either general linear systems or nonlinear oscillators. These nodes communicate over general network topology, and the nodes from different clusters are governed by different self-dynamics. A unified convergence analysis is provided to analyze the synchronization via intermittent pinning controllers. It is observed that the nodes in different clusters synchronize to the given patterns if a directed spanning tree exists in the underlying topology of every extended cluster (which consists of the original cluster of nodes as well as their pinning node) and one algebraic condition holds. Structural conditions are then derived to guarantee such an algebraic condition. That is: 1) if the intracluster couplings are with sufficiently strong strength and the pinning controller is with sufficiently long execution time in every period, then the algebraic condition for general linear systems is warranted and 2) if every cluster is with the sufficiently strong intracluster coupling strength, then the pinning controller for nonlinear oscillators can have its execution time to be arbitrarily short. The lower bounds are explicitly derived both for these coupling strengths and the execution time of the pinning controller in every period. In addition, in regard to the above-mentioned structural conditions for nonlinear systems, an adaptive law is further introduced to adapt the intracluster coupling strength, such that the cluster synchronization for nonlinear systems is achieved.

Consensus Control of Nonlinear Multiagent Systems With Time-Varying State Constraints

In this paper, we present a novel adaptive consensus algorithm for a class of nonlinear multiagent systems with time-varying asymmetric state constraints. As such, our contribution is a step forward beyond the usual consensus stabilization result to show that the states of the agents remain within a user defined, time-varying bound. To prove our new results, the original multiagent system is transformed into a new one. Stabilization and consensus of transformed states are sufficient to ensure the consensus of the original networked agents without violating of the predefined asymmetric time-varying state constraints. A single neural network (NN), whose weights are tuned online, is used in our design to approximate the unknown functions in the agent's dynamics. To account for the NN approximation residual, reconstruction error, and external disturbances, a robust term is introduced into the approximating system equation. Additionally in our design, each agent only exchanges the information with its neighbor agents, and thus the proposed consensus algorithm is decentralized. The theoretical results are proved via Lyapunov synthesis. Finally, simulations are performed on a nonlinear multiagent system to illustrate the performance of our consensus design scheme.

Adaptive Fault-Tolerant Synchronization Control of a Class of Complex Dynamical Networks With General Input Distribution Matrices and Actuator Faults

This paper is concerned with the problem of adaptive fault-tolerant synchronization control of a class of complex dynamical networks (CDNs) with actuator faults and unknown coupling weights. The considered input distribution matrix is assumed to be an arbitrary matrix, instead of a unit one. Within this framework, an adaptive fault-tolerant controller is designed to achieve synchronization for the CDN. Moreover, a convex combination technique and an important graph theory result are developed, such that the rigorous convergence analysis of synchronization errors can be conducted. In particular, it is shown that the proposed fault-tolerant synchronization control approach is valid for the CDN with both time-invariant and time-varying coupling weights. Finally, two simulation examples are provided to validate the effectiveness of the theoretical results.

Graph Theory-Based Pinning Synchronization of Stochastic Complex Dynamical Networks

This paper is concerned with the adaptive pinning synchronization problem of stochastic complex dynamical networks (CDNs). Based on algebraic graph theory and Lyapunov theory, pinning controller design conditions are derived, and the rigorous convergence analysis of synchronization errors in the probability sense is also conducted. Compared with the existing results, the topology structures of stochastic CDN are allowed to be unknown due to the use of graph theory. In particular, it is shown that the selection of nodes for pinning depends on the unknown lower bounds of coupling strengths. Finally, an example on a Chua's circuit network is given to validate the effectiveness of the theoretical results.

Optimal Communication Network-Based H∞ Quantized Control With Packet Dropouts for a Class of Discrete-Time Neural Networks With Distributed Time Delay

This paper is concerned with optimal communication network-based H∞ quantized control for a discrete-time neural network with distributed time delay. Control of the neural network (plant) is implemented via a communication network. Both quantization and communication network-induced data packet dropouts are considered simultaneously. It is assumed that the plant state signal is quantized by a logarithmic quantizer before transmission, and communication network-induced packet dropouts can be described by a Bernoulli distributed white sequence. A new approach is developed such that controller design can be reduced to the feasibility of linear matrix inequalities, and a desired optimal control gain can be derived in an explicit expression. It is worth pointing out that some new techniques based on a new sector-like expression of quantization errors, and the singular value decomposition of a matrix are developed and employed in the derivation of main results. An illustrative example is presented to show the effectiveness of the obtained results.

Pinning Synchronization of Directed Networks With Switching Topologies: A Multiple Lyapunov Functions Approach

This paper studies the global pinning synchronization problem for a class of complex networks with switching directed topologies. The common assumption in the existing related literature that each possible network topology contains a directed spanning tree is removed in this paper. Using tools from M -matrix theory and stability analysis of the switched nonlinear systems, a new kind of network topology-dependent multiple Lyapunov functions is proposed for analyzing the synchronization behavior of the whole network. It is theoretically shown that the global pinning synchronization in switched complex networks can be ensured if some nodes are appropriately pinned and the coupling is carefully selected. Interesting issues of how many and which nodes should be pinned for possibly realizing global synchronization are further addressed. Finally, some numerical simulations on coupled neural networks are provided to verify the theoretical results.

Synchronization of neural networks with stochastic perturbation via aperiodically intermittent control

In this paper, the synchronization problem for neural networks with stochastic perturbation is studied with intermittent control via adaptive aperiodicity. Under the framework of stochastic theory and Lyapunov stability method, we develop some techniques of intermittent control with adaptive aperiodicity to achieve the synchronization of a class of neural networks, modeled by stochastic systems. Some effective sufficient conditions are established for the realization of synchronization of the underlying network. Numerical simulations of two examples are provided to illustrate the theoretical results obtained in the paper.

Impulsive stabilization and impulsive synchronization of discrete-time delayed neural networks

This paper investigates the problems of impulsive stabilization and impulsive synchronization of discrete-time delayed neural networks (DDNNs). Two types of DDNNs with stabilizing impulses are studied. By introducing the time-varying Lyapunov functional to capture the dynamical characteristics of discrete-time impulsive delayed neural networks (DIDNNs) and by using a convex combination technique, new exponential stability criteria are derived in terms of linear matrix inequalities. The stability criteria for DIDNNs are independent of the size of time delay but rely on the lengths of impulsive intervals. With the newly obtained stability results, sufficient conditions on the existence of linear-state feedback impulsive controllers are derived. Moreover, a novel impulsive synchronization scheme for two identical DDNNs is proposed. The novel impulsive synchronization scheme allows synchronizing two identical DDNNs with unknown delays. Simulation results are given to validate the effectiveness of the proposed criteria of impulsive stabilization and impulsive synchronization of DDNNs. Finally, an application of the obtained impulsive synchronization result for two identical chaotic DDNNs to a secure communication scheme is presented.

Synchronization of nonlinear coupled networks via aperiodically intermittent pinning control

In this paper, pinning synchronization problem for nonlinear coupled networks is investigated, which can be recurrently connected neural networks, cellular neural networks, Hodgkin-Huxley models, Lorenz chaotic oscillators, and so on. Nodes in the network are assumed to be identical and nodes' dynamical behaviors are described by continuous-time equations. The network topology is undirected and static. At first, the scope of accepted nonlinear coupling functions is defined, and the effect of nonlinear coupling functions on synchronization is carefully discussed. Then, the pinning control technique is used for synchronization, especially the control type is aperiodically intermittent. Some sufficient conditions to guarantee global synchronization are presented. Furthermore, the adaptive approach is also applied on the pinning control, and a centralized adaptive algorithm is designed and its validity is also proved. Finally, several numerical simulations are given to verify the obtained theoretical results.

Pinning synchronization of coupled inertial delayed neural networks

The paper is devoted to the investigation of synchronization for an array of linearly and diffusively coupled inertial delayed neural networks (DNNs). By placing feedback control on a small fraction of network nodes, the entire coupled DNNs can be synchronized to a common objective trajectory asymptotically. Two different analysis methods, including matrix measure strategy and Lyapunov-Krasovskii function approach, are employed to provide sufficient criteria for the synchronization control problem. Comparisons of these two techniques are given at the end of the paper. Finally, an illustrative example is provided to show the effectiveness of the obtained theoretical results.

Pinning distributed synchronization of stochastic dynamical networks: a mixed optimization approach

This paper is concerned with the problem of pinning synchronization of nonlinear dynamical networks with multiple stochastic disturbances. Two kinds of pinning schemes are considered: 1) pinned nodes are fixed along the time evolution and 2) pinned nodes are switched from time to time according to a set of Bernoulli stochastic variables. Using Lyapunov function methods and stochastic analysis techniques, several easily verifiable criteria are derived for the problem of pinning distributed synchronization. For the case of fixed pinned nodes, a novel mixed optimization method is developed to select the pinned nodes and find feasible solutions, which is composed of a traditional convex optimization method and a constraint optimization evolutionary algorithm. For the case of switching pinning scheme, upper bounds of the convergence rate and the mean control gain are obtained theoretically. Simulation examples are provided to show the advantages of our proposed optimization method over previous ones and verify the effectiveness of the obtained results.

Impulsive control for synchronizing delayed discrete complex networks with switching topology

In this paper, global exponential synchronization of a class of discrete delayed complex networks with switching topology has been investigated by using Lyapunov-Ruzimiki method. The impulsive scheme is designed to work at the time instant of switching occurrence. A time-varying delay-dependent criterion for impulsive synchronization is given to ensure the delayed discrete complex networks switching topology tending to a synchronous state. Furthermore, a numerical simulation is given to illustrate the effectiveness of main results

M-matrix strategies for pinning-controlled leader-following consensus in multiagent systems with nonlinear dynamics

This paper considers the leader-following consensus problem for multiagent systems with inherent nonlinear dynamics. Some M-matrix strategies are developed to address several challenging issues in the pinning control of multiagent systems by using algebraic graph theory and the properties of nonnegative matrices. It is shown that second-order leader-following consensus in a nonlinear multiagent system can be reached if the virtual leader has a directed path to every follower and a derived quantity is greater than a positive threshold. In particular, this paper analytically proves that leader-following consensus may be easier to be achieved by pinning more agents or increasing the pinning feedback gains. A selective pinning scheme is then proposed for nonlinear multiagent systems with directed network topologies. Numerical results are given to verify the theoretical analysis.

Exponential stabilization of delayed recurrent neural networks: A state estimation based approach

This paper is concerned with the stabilization problem of delayed recurrent neural networks. As the states of neurons are usually difficult to be fully measured, a state estimation based approach is presented. First, a sufficient condition is derived such that the augmented system under consideration is globally exponentially stable. Then, by employing a decoupling technique, the gain matrices of the controller and state estimator are achieved by solving some linear matrix inequalities. Finally, a delayed neural network with chaotic behaviors is exploited to demonstrate the applicability of the developed result.

On stabilization of stochastic Cohen-Grossberg neural networks with mode-dependent mixed time-delays and Markovian switching

The globally exponential stabilization problem is investigated for a general class of stochastic Cohen-Grossberg neural networks with both Markovian jumping parameters and mixed mode-dependent time-delays. The mixed time-delays consist of both discrete and distributed delays. This paper aims to design a memoryless state feedback controller such that the closed-loop system is stochastically exponentially stable in the mean square sense. By introducing a new Lyapunov-Krasovskii functional that accounts for the mode-dependent mixed delays, stochastic analysis is conducted in order to derive delay-dependent criteria for the exponential stabilization problem. Three numerical examples are carried out to demonstrate the feasibility of our delay-dependent stabilization criteria.

Multiobjective identification of controlling areas in neuronal networks

In this paper, we investigate the multiobjective identification of controlling areas in the neuronal network of a cat's brain by considering two measures of controllability simultaneously. By utilizing nondominated sorting mechanisms and composite differential evolution (CoDE), a reference-point-based nondominated sorting composite differential evolution (RP-NSCDE) is developed to tackle the multiobjective identification of controlling areas in the neuronal network. The proposed RP-NSCDE shows its promising performance in terms of accuracy and convergence speed, in comparison to nondominated sorting genetic algorithms II. The proposed method is also compared with other representative statistical methods in the complex network theory, single objective, and constraint optimization methods to illustrate its effectiveness and reliability. It is shown that there exists a tradeoff between minimizing two objectives, and therefore pareto fronts (PFs) can be plotted. The developed approaches and findings can also be applied to coordination control of various kinds of real-world complex networks including biological networks and social networks, and so on.