Publications

In this paper, stability analysis and decentralized control problems are addressed for linear and sector-nonlinear complex dynamical networks. Necessary and sufficient conditions for stability and stabilizability under a special decentralized control strategy are given for linear networks. Especially, two types of linear regular networks, star-shaped networks and globally coupled networks, are studied in detail. A dynamical network is viewed as a large-scale system composing of some subsystems, based on which the relationship between the stability of a network and the stability of its corresponding subsystems is investigated. It is pointed out that some subsystems must be unstable for the whole network to be stable in some special cases. Moreover, a controller design method based on a parameter-dependent Lyapunov function is provided. Furthermore, interconnected Lur’e systems and symmetrical networks of Lur’e systems are similarly studied. The test of absolute stability of a network of Lur’e systems is separated into the test of absolute stability of several independent Lur’e systems. Finally, several numerical examples are given to illustrate the theoretical results.

This study concerns the consensus of a network of agents with general linear or linearised dynamics, whose communication topology contains a directed spanning tree. An observer-type consensus protocol based on the relative outputs of the neighbouring agents is adopted. The notion of consensus region is introduced, as a measure for the robustness of the protocol and as a basis for the protocol design. For neutrally stable agents, it is shown that there exists a protocol achieving consensus together with a consensus region that is the entire open right-half plane if and only if each agent is stabilisable and detectable. An algorithm is further presented for constructing such a protocol. For consensus with a prescribed convergence speed, a multi-step protocol design procedure is given, which yields an unbounded consensus region and at the same time maintains a favourable decoupling property. Finally, the consensus algorithms are extended to solve the formation control problems.

In this Letter, a dynamical delayed output-feedback (DDOF) control strategy is proposed for stabilizing unstable periodic orbits (UPOs) of chaotic systems. Using the Floquet theory, a separation principle is established which gives a necessary and sufficient stability condition for DDOF UPO stabilizing control systems. The new principle shows that the so-called “odd number limitation” for delayed state-feedback control systems also applies to DDOF control.

Summary This paper addresses the finite‐time formation tracking problem for multiple vehicles with dynamics model on SE(3) (the specific Euclidean group of rigid body motions), under the condition that the tracking time is preassigned according to the task requirements. By using Pontryagin's maximum principle on Lie groups, a class of finite‐time optimal tracking control laws are designed for vehicles to track a desired trajectory within a given finite time. Meanwhile, the corresponding cost function is minimized. Furthermore, a tracking‐time lower bound is derived for multi‐vehicle systems with control constraints. Finally, an illustrative example is provided to demonstrate the effectiveness of the proposed control laws. Copyright © 2015 John Wiley & Sons, Ltd.

In this letter, a new hyperchaotic system is formulated by introducing an additional state into the third-order generalized Lorenz equation. The existence of the hyperchaos is verified with bifurcation analysis, and the bifurcation routes from periodic, quasi-periodic, chaotic and hyperchaotic evolutions are observed. Various attractors are illustrated not only by computer simulation but also by the realization of an electronic circuit. Copyright © 2005 John Wiley & Sons, Ltd.

Let ( H , d ) be a metric space, F be a Furstenberg family, and ( g m ) m ∈ Z + be a sequence of continuous map on H, which converges uniformly to a map g on H. In this paper, under the condition lim m → ∞ ⁡ d ∞ ( g m m , g m ) = 0 , a necessary and sufficient condition for g to be F -mixing is established. Moreover, let T ⊂ Z + be an infinite set and lim m ∈ T : m → ∞ ⁡ d ∞ ( g m m , g m ) = 0 . Then, some necessary and sufficient conditions, or sufficient conditions, for g to be some stronger forms of topological transitivity, sensitivity, ergodic, or mixing are obtained.

In this article, the global consensus problem of ring-networked nonholonomic systems with a saturated input is considered. Based on the Lyapunov method and appropriate related technologies, the stabilization of the nonholonomic systems is achieved toward consensus. Assuming that each agent has its own position information available in the global coordinates and can obtain the position information of its neighbors, global consensus is achieved asymptotically by using the designed distributed saturated controllers. A wireless local area network is set up with a local computer as the controller, having data transmitted through the wireless network so that the movement of the robots can be controlled. Consistent simulation and experimental results are presented to illustrate the practical design and theoretical analysis.

No abstract is provided for this article.

Today, complex networks have attracted increasing attention from various fields of science and engineering. It has been demonstrated that many complex networks display various synchronization phenomena. In this note, we introduce a time-varying complex dynamical network model. We then further investigate its synchronization phenomenon and prove several network synchronization theorems. Especially, we show that synchronization of such a time-varying dynamical network is completely determined by the inner-coupling matrix, and by the eigenvalues and the corresponding eigenvectors of the coupling configuration matrix of the network.

We apply the theory of incremental input-to-state stability to the problem of synchronization in a complex dynamical network of identical nodes, using chaotic nodes as a typical platform. The proposed technique can achieve chaos synchronization using only partial state/output information in the sense that it does not require all nodes to have access to the state/output information from the seed node that produces the reference orbit for network synchronization. Examples and simulations demonstrate the applicability and effectiveness of the new synchronization method.

No abstract is provided for this article.

No abstract is provided for this article.

Understanding the driving forces behind the Internet evolution is critical, which can provide benefits to construct more realistic Internet models with more comprehensive Internet simulations. In most of the Internet modeling mechanisms proposed so far, e.g. the preferential attachment rule, some basic structural properties such as the node and edge connectivities play the key roles in forming the network structure. Very few works to date have explored the effects of socio-economic factors on the formation and evolution of the Internet structure. In this paper, the China Internet structure is investigated, on the city level, showing that the constructed network is a highly heterogeneous network with small-world features. Then, the effect and impact of socioeconomic factors on the city-level China Internet structure is explored, including population, population growth rate, gross domestic product (GDP) and GDP per Capita. It is shown that population, population growth rate and GDP per Capita are weakly correlated to the connectivity of cities. Strikingly, GDP of a city is highly related to its connectivity in the network. The higher the GDP of a city, the higher the probability to attract connections from other cities. The new findings reveal that GDP is a good indicator for the scaling of the Internet at the city level.

In the semi-supervised setting where labeled data are largely limited, it remains to be a big challenge for message passing based graph neural networks (GNNs) to learn feature representations for the nodes with the same class label that is distributed discontinuously over the graph. To resolve the discontinuous information transmission problem, we propose a control principle to supervise representation learning by leveraging the prototypes (i.e., class centers) of labeled data. Treating graph learning as a discrete dynamic process and the prototypes of labeled data as "desired" class representations, we borrow the pinning control idea from automatic control theory to design learning feedback controllers for the feature learning process, attempting to minimize the differences between message passing derived features and the class prototypes in every round so as to generate class-relevant features. Specifically, we equip every node with an optimal controller in each round through learning the matching relationships between nodes and the class prototypes, enabling nodes to rectify the aggregated information from incompatible neighbors in a graph with strong heterophily. Our experiments demonstrate that the proposed PCGCN model achieves better performances than deep GNNs and other competitive heterophily-oriented methods, especially when the graph has very few labels and strong heterophily.

No abstract is provided for this article.