Global Robust Synchronization Research Articles

Global robust exponential synchronization of neutral-type interval Cohen–Grossberg neural networks with mixed time delays

Global robust exponential synchronization of neutral-type interval Cohen–Grossberg neural networks (NTICGNNs) with mixed time delays is analyzed in this paper. The system model, in which unrepresentable using vector-matrices, renders certain methods unsuitable for addressing issues within the vector-matrix framework. To address this limitation, a direct method based on system solutions is proposed, and sufficient conditions are provided to achieve global robust exponential synchronization of the considered NTICGNNs. This approach results in a global robust exponential synchronization criterion without the need to establish any Lyapunov-Krasovskii functionals. The applicability of the obtained synchronization conditions is validated using two numerical examples. Additionally, the obtained theoretical results have been applied to solve a quadratic programming problem and to encrypt and decrypt color images, demonstrating the practical application value of our research results. Notably, this study presents the first global robust exponential synchronization analysis for the considered NTICGNNs and proposes a novel approach grounded in system solutions.

Global Robust Exponential Synchronization of Interval BAM Neural Networks with Multiple Time-Varying Delays

Global Robust Exponential Synchronization of Interval BAM Neural Networks with Multiple Time-Varying Delays

Robust synchronization in finite time for fractional-order hybrid coupling discontinuous complex dynamic networks with nonlinear growth

In this paper, the global robust synchronization and synchronization in finite time are considered for fractional-order hybrid coupling complex dynamical networks (CDNs), where the growth of dynamic nodes is discontinuous, and subjected to a quadratic polynomial. Firstly, a convergence principle in finite time is developed for fractional-order nonlinear systems with discontinuous right-hand side. Secondly, a suitable discontinuous controller without the terms of time delays is designed, and the global robust synchronization condition is addressed in the terms of linear matrix inequalities (LMIs) by applying Lyapunov functional approach, inequality analysis technique, and Clarke’s non-smooth analysis method. In addition, the global robust synchronization goal in finite time is achieved by utilizing the developed convergence principle. Moreover, the upper bound of the settling time for the global robust synchronization in finite time is explicitly evaluated. Finally, the feasibility of the proposed design scheme and the validity of theoretical results are verified by two numerical simulation examples.

Global Robust Synchronization of Fractional Order Complex Valued Neural Networks with Mixed Time Varying Delays and Impulses

In this article, we explore the theoretical issues on the drive-response synchronization of a class of fractional order uncertain complex valued neural networks (FOUCNNs) with mixed time varying delays and impulses. Based upon the contraction mapping principle, robust analysis techniques, as well as Riemann-Liouville (R-L) derivative, we derive a new set of novel sufficient conditions for the existence and uniqueness of equilibrium point of such neural network system, while by applying the Lyapunov functional approach, the global stability of the equilibrium solutions are obtained. Furthermore, the synchronization criterion of FOUCNNs is also attracted by means of the adaptive error feedback control strategy. Finally, two examples are provided along with the simulation results to demonstrate the effectiveness of our main proofs.

Global Robust Exponential Synchronization of Multiple Uncertain Neural Networks Subject to Event‐Triggered Strategy

This paper proposes the event‐triggered strategy (ETS) for multiple neural networks (NNs) with parameter uncertainty and time delay. By establishing event‐triggered mechanism and using matrix inequality techniques, several sufficient criteria are obtained to ensure global robust exponential synchronization of coupling NNs. In particular, the coupling matrix need not be the Laplace matrix in this paper. In addition, the lower bounds of sampling time intervals are also found by the established event‐triggered mechanism. Eventually, three numerical examples are offered to illustrate the obtained results.

Robust synchronization of discontinuous Cohen–Grossberg neural networks: Pinning control approach

In this issue, the robust synchronization for a class of uncertain Cohen–Grossberg neural networks is studied, in which neuron activations are modelled by discontinuous functions(or piecewise continuous functions). Pinning state-feedback and adaptive controllers are designed to achieve global robust exponential synchronization and global robust asymptotical synchronization of drive-response-based discontinuous Cohen–Grossberg neural networks. By applying the theory of non-smooth analysis theory and the method of generalized Lyapunov functional, some criteria are given to show that the coupled discontinuous Cohen–Grossberg neural networks with parameter uncertainties can realized global robust synchronization. Some examples and numerical simulations are also shown to verify the validity of the proposed results.

Robust output synchronization of heterogeneous nonlinear agents in uncertain networks

This paper investigates the global robust output synchronization problem for a class of nonlinear multi-agent systems. In the considered setup, the controlled agents are heterogeneous and with both dynamic and parametric uncertainties, the controllers are incapable of exchanging their internal states with the neighbors, and the communication network among agents is defined by an uncertain simple digraph. The problem is pursued via nonlinear output regulation theory and internal model based design. For each agent, the input-driven filter and the internal model compose the controller, and the decentralized dynamic output feedback control law is derived by using backstepping method and the modified dynamic high-gain technique. The theoretical result is applied to output synchronization problem for uncertain network of Lorenz-type agents.

Robust Synchronization of Multiple Memristive Neural Networks With Uncertain Parameters via Nonlinear Coupling

This paper is concerned with the global robust synchronization of multiple memristive neural networks (MMNNs) with nonidentical uncertain parameters. A coupling scheme is introduced, in a general topological structure described by a direct or undirect graph, with a linear diffusive term and a discontinuous sign term. First, a set of sufficient conditions are derived based on the Lyapunov stability theory for ascertaining global robust synchronization of coupled MMNNs. Second, a pinning adaptive coupling method is proposed to ensure global synchronization without knowing the bound of parameter uncertainties. Two illustrative examples are discussed to substantiate the theoretical results.

Global robust exponential synchronization of BAM recurrent FNNs with infinite distributed delays and diffusion terms on time scales

In this article, the global robust exponential synchronization of reaction-diffusion BAM recurrent fuzzy neural networks (FNNs) with infinite distributed delays on time scales is investigated. Applied Lyapunov functional and inequality skills, some sufficient criteria are established to guarantee the global robust exponential synchronization of reaction-diffusion BAM recurrent FNNs with infinite distributed delays on time scales. One example is given to illustrate the effectiveness of our results.

Adaptive Control for Modified Projective Synchronization-Based Approach for Estimating All Parameters of a Class of Uncertain Systems: Case of Modified Colpitts Oscillators

A method of estimation of all parameters of a class of nonlinear uncertain dynamical systems is considered, based on the modified projective synchronization (MPS). The case of modified Colpitts oscillators is investigated. Through a suitable transformation of the dynamical system, sufficient conditions for achieving synchronization are derived based on Lyapunov stability theory. Global stability and asymptotic robust synchronization of the considered system are investigated. The proposed approach offers a systematic design procedure for robust adaptive synchronization of a large class of chaotic systems. The combined effect of both an additive white Gaussian noise (AWGN) and an artificial perturbation is numerically investigated. Results of numerical simulations confirm the effectiveness of the proposed control strategy.

Robust Fault Detection during the Synchronization Process of Nonlinear Lur'e Dynamical Networks

The present study focuses on the robust fault detection issue within the synchronization process of nonlinear Lur'e dynamical networks. Sufficient conditions in terms of linear matrix inequalities (LMIs) are established to guarantee global robust synchronization of the network. Under such a synchronization scheme, the error dynamical system is globally asymptotically stable, the effect of external disturbances is suppressed, and at the same time, the network is sensitive to possible faults based on a mixedperformance.

Global robust synchronization for time-varying phase mismatching electro-mechanical gyrostat systems under variable substitution control

A master–slave scheme for global robust synchronization of two electro-mechanical gyrostat systems with time-varying phase mismatches under variable substitution control is presented in this paper. Under this scheme, a sufficient criterion for the global robust synchronization with bounded error is rigorously proved in the form of matrix inequality and the corresponding estimated error bound is mathematically given. On the basis of the criterion, further derivation brings some simple and optimized algebraic criteria for various single-variable coupling, whose performance is then verified through some numerical examples.

GLOBAL ROBUST SYNCHRONIZATION OF A CLASS OF NONAUTONOMOUS CHAOTIC SYSTEMS WITH PARAMETER MISMATCH VIA VARIABLE SUBSTITUTION CONTROL

This paper investigates global robust synchronization of a class of nonautonomous chaotic systems with parameter mismatch under the master–slave variable substitution control. A criterion of linear matrix inequality (LMI) for the global robust synchronization is rigorously proven and the corresponding synchronization error bound is analytically estimated. The LMI criterion is then applied to the gyrostat systems, obtaining some simple and optimized algebraic criteria for global robust synchronization of the master–slave gyrostat systems with time-varying phase mismatch under single-variable substitution configurations, further verified in a numerical example.

The sufficient criteria for global synchronization of chaotic power systems under linear state-error feedback control

This paper investigates global complete synchronization of two identical power systems and global robust synchronization of two power systems with parameter mismatch and external disturbance, both under the master–slave linear state-error feedback control. Some criteria for achieving the synchronization via a single-variable linear coupling are derived and formulated in simple algebraic inequalities. These algebraic criteria are further optimized so as to improve their performances. The effectiveness of the new algebraic criteria is illustrated by the numerical examples.

Global exponential synchronization of stochastic switching networks with time-varying delay

This paper is concerned with the global exponential synchronization of stochastic delayed switching networks via hybrid control. The network under investigation is quite general to reflect the reality, where the network topology consists of r modes and switches from one mode to another according to a Markovian chain with known transition probability. Parameter uncertainties, time varying delay and stochastic disturbances are all taken into account in this study. Based on the Lyapunov functional method and stochastic analysis techniques, some new criteria for the global robust synchronization via hybrid control are established. Finally, one example with numerical simulation is given for illustration. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society

A global asymptotic synchronization problem via internal model approach

In this paper, we study the global robust synchronization problem of the controlled Duffing system and the van der Pol oscillator. By employing the internal model approach, we first convert the problem into a global robust stabilization problem of a time-varying nonlinear system in the lower triangular form. Then we show that the global robust stabilization problem of the lower triangular system is solvable, thus leading to the solution of the global robust synchronization problem.

Global Robust Stability and Synchronization of Networks With Lorenz-Type Nodes

This brief addresses in a unified framework both global robust stability and synchronization problems for a class of directed networks with Lorenz-type nodes. When the key parameter in the node equation is modified, it covers the Lorenz, Chen, and Lu types of networks as special cases. Based on an observation about some special nonlinear characteristics of Lorenz-type systems, simple conditions are derived for global stability and synchronization of such networks, where the typical Lipschitz-type condition for nonlinear functions is not needed. By combining the pinning control strategy and a new linear control law, synchronization of a network with different nodes can be achieved. Several examples are given for illustration.

Robust adaptive synchronization of chaotic neural networks by slide technique

In this paper, we focus on the robust adaptive synchronization between two coupled chaotic neural networks with all the parameters unknown and time-varying delay. In order to increase the robustness of the two coupled neural networks, the key idea is that a sliding-mode-type controller is employed. Moreover, without the estimate values of the network unknown parameters taken as an updating object, a new updating object is introduced in the constructing of controller. Using the proposed controller, without any requirements for the boundedness, monotonicity and differentiability of activation functions, and symmetry of connections, the two coupled chaotic neural networks can achieve global robust synchronization no matter what their initial states are. Finally, the numerical simulation validates the effectiveness and feasibility of the proposed technique.

Synchronization of neural networks based on parameter identification and via output or state coupling

For neural networks with all the parameters unknown, we focus on the global robust synchronization between two coupled neural networks with time-varying delay that are linearly and unidirectionally coupled. First, we use Lyapunov functionals to establish general theoretical conditions for designing the coupling matrix. Neither symmetry nor negative (positive) definiteness of the coupling matrix are required; under less restrictive conditions, the two coupled chaotic neural networks can achieve global robust synchronization regardless of their initial states. Second, by employing the invariance principle of functional differential equations, a simple, analytical, and rigorous adaptive feedback scheme is proposed for the robust synchronization of almost all kinds of coupled neural networks with time-varying delay based on the parameter identification of uncertain delayed neural networks. Finally, numerical simulations validate the effectiveness and feasibility of the proposed technique.