Distributed Extended State Estimation for Complex Networks With Nonlinear Uncertainty

This article studies the distributed state estimation issue for complex networks with nonlinear uncertainty. The extended state approach is used to deal with the nonlinear uncertainty. The distributed state predictor is designed based on the extended state system model, and the distributed state estimator is designed by using the measurement of the corresponding node. The prediction error and the estimation error are derived. The prediction error covariance (PEC) is obtained in terms of the recursive Riccati equation, and the upper bound of the PEC is minimized by designing an optimal estimator gain. With the vectorization approach, a sufficient condition concerning stability of the upper bound is developed. Finally, a numerical example is presented to illustrate the effectiveness of the designed extended state estimator.

FLS-Based Adaptive Synchronization Control of Complex Dynamical Networks With Nonlinear Couplings and State-Dependent Uncertainties

This paper is concerned with the problem of synchronization control of complex dynamical networks (CDN) subject to nonlinear couplings and uncertainties. An fuzzy logical system-based adaptive distributed controller is designed to achieve the synchronization. The asymptotic convergence of synchronization errors is analyzed by combining algebraic graph theory and Lyapunov theory. In contrast to the existing results, the proposed synchronization control method is applicable for the CDN with system uncertainties and unknown topology. Especially, the considered uncertainties are allowed to occur in the node local dynamics as well as in the interconnections of different nodes. In addition, it is shown that a unified controller design framework is derived for the CDN with or without coupling delays. Finally, simulations on a Chua's circuit network are provided to validate the effectiveness of the 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.

Globally exponential synchronization and synchronizability for general dynamical networks

The globally exponential synchronization problem for general dynamical networks is considered in this paper. One quantity will be distilled from the coupling matrix to characterize the synchronizability of the corresponding dynamical networks. The calculation of such a quantity is very convenient even for large-scale networks. The network topology is assumed to be directed and weakly connected, which implies that the coupling configuration matrix can be asymmetric, weighted, or reducible. This assumption is more consistent with the realistic network in practice than the constraint of symmetry and irreducibility. By using the Lyapunov functional method and the Kronecker product techniques, some criteria are obtained to guarantee the globally exponential synchronization of general dynamical networks. In addition, numerical examples, including small-world and scale-free networks, are given to demonstrate the theoretical results. It will be shown that our criteria are available for large-scale dynamical networks.

Coordinate transformation and matrix measure approach for synchronization of complex networks

Global synchronization in complex networks has attracted considerable interest in various fields. There are mainly two analytical approaches for studying such time-varying networks. The first approach is Lyapunov function-based methods. For such an approach, the connected-graph-stability (CGS) method arguably gives the best results. Nevertheless, CGS is limited to the networks with cooperative couplings. The matrix measure approach (MMA) proposed by Chen, although having a wider range of applications in the network topologies than that of CGS, works for smaller numbers of nodes in most network topologies. The approach also has a limitation with networks having partial-state coupling. Other than giving yet another MMA, we introduce a new and, in some cases, optimal coordinate transformation to study such networks. Our approach fixes all the drawbacks of CGS and MMA. In addition, by merely checking the structure of the vector field of the individual oscillator, we shall be able to determine if the system is globally synchronized. In summary, our results can be applied to rather general time-varying networks with a large number of nodes.

Generalized synchronization of complex networks

We consider generalized synchronization of complex networks, which are unidirectionally coupled in the drive-response configuration. The drive network consists of linearly and diffusively coupled identical chaotic systems. By choosing suitable driving signals, we can construct the response network to generally synchronize the drive network in a predefined functional relationship. This extends both generalized synchronization of chaotic systems and synchronization inside a network. Theoretical analysis and numerical simulations fully verify our main results.

Matrix-measure criterion for synchronization in coupled-map networks

We present conditions for the local and global synchronization in coupled-map networks using the matrix measure approach. In contrast to many existing synchronization conditions, the proposed synchronization criteria do not depend on the solution of the synchronous state and give less limitation on the network connections. Numerical simulations of the coupled quadratic maps demonstrate the potentials of our main results.

Generalized synchronization of chaotic systems: an auxiliary system approach via matrix measure

In this paper, generalized synchronization of two chaotic systems is investigated. The auxiliary system approach, which is suggested by H. Abarbanel, N. Rulkov, and M. Sushchik [Phys. Rev. E 53, 4528 (1996)], is used to detect and study generalized synchronization. Based on the Lyapunov method and matrix measure, some less restrictive criteria are obtained to guarantee the asymptotical stability of the error system between the response system and the auxiliary system, which indicates the drive-response systems are synchronized in a general sense. It is shown that the feedback gain can be reduced by means of the matrix measure approach, compared to the norm method. All theoretical results are illustrated by analytical and numerical examples.

Global synchronization in lattices of coupled chaotic systems

Based on the concept of matrix measures, we study global stability of synchronization in networks. Our results apply to quite general connectivity topology. In addition, a rigorous lower bound on the coupling strength for global synchronization of all oscillators is also obtained. Moreover, by merely checking the structure of the vector field of the single oscillator, we shall be able to determine if the system is globally synchronized.

Synchronization in time-varying networks: a matrix measure approach

Synchronization in complex networks has attracted lots of interest in various fields. We consider synchronization in time-varying networks, in which the weights of links are time varying. We propose a useful approach--i.e., the matrix measure approach--to derive some analytically sufficient conditions for synchronization in time-varying networks. These conditions are less conservative than many existing synchronization conditions. Theoretical analysis and numerical simulations of different networks verify our main results.