Publications

A NEW CHAOTIC SYSTEM AND ITS GENERATION

This Letter introduces a relatively simple three-dimensional continuous autonomous chaotic system, which can display complex 2- and 4-scroll attractors in simulations. Its generation and basic dynamical behaviors are briefly described.

Optimal Synchronizability of Complex Networks

No abstract is provided for this article.

ON GLOBAL EXPONENTIAL SYNCHRONIZATION OF CHUA CIRCUITS

This paper develops a theory of global exponential synchronization using two Chua circuits as the platform, for which five theorems are established by constructing new Lyapunov functions and employing the comparison principle in conjunction with the stability theory with respect to partial components.

IEEE Awards

For his pioneering and lifelong research contributions, particularly in multidimensional signal processing, distributed parameters networks, graph theory, discrete transforms and image processing.For nearly six decades of outstanding contributions to education and for lifelong dedication to the service of the CAS Society

高次元自律系におけるNeimark-Sacker 分岐の一計算法

自律系にみられるリミットサイクルにおいて，パラメータの変化により特性乗数が複素単位円を横切る場合，Neimark-Sacker分岐を生じる．本論文ではこの分岐パラメータ値を求める新しい計算方法を提案する．固定点条件，Poincaré断面条件に加えて，共役複素数の特性乗数を代入した特性方程式を実部と虚部に分離し，それぞれを独立した条件として採用する．これら条件式を連立させ，ニュートン法により解く．新たな独立変数として，共役複素な特性乗数の偏角を用いた．ニュートン法のヤコビ行列の各要素は，複素数演算，数値微分を用いることなく，変分方程式の解と行列操作によって求めることができるため，ニュートン法の収束性もよい．例として8次元自律系のリミットサイクルのNeimark-Sacker分岐の計算結果をあげる．

Microscopic evaluation of traffic safety at signal coordinated intersections: A before–after study

Objective: This research aims to evaluate the safety impacts of signal coordination on signalized intersections and provide a scientific basis to design and improve signal control and management from a traffic safety perspective.Methods: A kernel regression model is adopted to evaluate the safety performance of intersections before and after implementing the signal coordination strategy. By using this statistical method, the authors identify the nonlinear relationship between crash frequency and the crash's spatial location and examine the discrepancy of crash spatial distributions between the coordination and noncoordination conditions at disaggregated levels, such as time of day and crash type. A case study is presented with the use of Michigan crash data (2003–2007).Results: The study finds that the (1) crash distribution on arterials tends to be spatially disperse when the signal coordination is in operation and (2) crash frequency at the approaches of intersections is increased with the use of signal coordination under the following conditions: Nonpeak hours, rear-end and sideswipe crashes, intersections with low speed limits, and both injury and property damage–only crashes.Conclusion: Signal coordination poses safety concerns in addition to its operational benefits for intersections.

Models and dynamics of deterministically growing networks

No abstract is provided for this article.

Controlling chaotic trajectories to unstable limit cycles - A case study

In the last two years, we have developed some new ideas and techniques for the control of chaotic nonlinear systems using conventional feedback controllers design methods, for both discrete-time and continuous-time systems [1-4], where the target position is either an (unstable) equilibrium point or an (unstable) limit cycle of the chaotic system. In this paper, we further provide a rigorous mathematical theory to support these new ideas and techniques, for a particular yet representative case: the well-known continuous-time chaotic Duffing system.

Counting spanning trees in self-similar networks by evaluating determinants

Spanning trees are relevant to various aspects of networks. Generally, the number of spanning trees in a network can be obtained by computing a related determinant of the Laplacian matrix of the network. However, for a large generic network, evaluating the relevant determinant is computationally intractable. In this paper, we develop a fairly generic technique for computing determinants corresponding to self-similar networks, thereby providing a method to determine the numbers of spanning trees in networks exhibiting self-similarity. We describe the computation process with a family of networks, called $(x,y)$-flowers, which display rich behavior as observed in a large variety of real systems. The enumeration of spanning trees is based on the relationship between the determinants of submatrices of the Laplacian matrix corresponding to the $(x,y)$-flowers at different generations and is devoid of the direct laborious computation of determinants. Using the proposed method, we derive analytically the exact number of spanning trees in the $(x,y)$-flowers, on the basis of which we also obtain the entropies of the spanning trees in these networks. Moreover, to illustrate the universality of our technique, we apply it to some other self-similar networks with distinct degree distributions, and obtain explicit solutions to the numbers of spanning trees and their entropies. Finally, we compare our results for networks with the same average degree but different structural properties, such as degree distribution and fractal dimension, and uncover the effect of these topological features on the number of spanning trees.

The sequence as a complex network

In this paper, a new topological approach for studying a sufficiently long random number sequence is proposed. By segmenting the sequence into groups of digits which represent the node identities while the undirected edges symbolize the adjacency between them, a network is constructed for analysis. In particular, the network constructed from a π sequence is examined in detail and its properties are contrasted with the Erdos–Renyi (ER) random graph model. Based on the observation that there are more nodes with even degrees than the adjacent odd counterparts in the constructed network, a new random graph model named Random Eulerian (RE) model and its extension are finally proposed and analyzed.

Answering an open problem on t-norms for type-2 fuzzy sets

This paper proves that a binary operation ⋆ on [0, 1], ensuring that the binary operation ⋏ is a t-norm or ⋎ is a t-conorm, is a t-norm, where ⋏ and ⋎ are special convolution operations defined by ( f ⋏ g ) ( x ) = sup { f ( y ) ★ g ( z ) : y ▵ z = x } , ( f ⋎ g ) ( x ) = sup { f ( y ) ★ g ( z ) : y ▿ z = x } , for any f, g ∈ Map([0, 1], [0, 1]), where △ and ▽ are a continuous t-norm and a continuous t-conorm on [0, 1], answering negatively an open problem posed in [8]. Besides, some characteristics of t-norm and t-conorm are obtained in terms of the binary operations ⋏ and ⋎.

Distributed Online Generalized Nash Equilibrium Learning in Multi-Cluster Games: A Delay-Tolerant Algorithm

No abstract is provided for this article.

A Distributed Optimization Scheme for State Estimation of Nonlinear Networks with Norm-bounded Uncertainties

This paper investigates the state estimation problem for a class of complex networks, in which the dynamics of each node is subject to Gaussian noise, system uncertainties and nonlinearities. Based on a regularized least-squares approach, the estimation problem is reformulated as an optimization problem, solving for a solution in a distributed way by utilizing a decoupling technique. Then, based on this solution, a class of estimators is designed to handle the system dynamics and constraints. A novel feature of this design lies in the unified modeling of uncertainties and nonlinearities, the decoupling of nodes, and the construction of recursive approximate covariance matrices for the optimization problem. Furthermore, the feasibility of the proposed estimators and the boundedness of the mean-square errors are ensured under a developed criterion, which is easier to check than some typical estimation strategies including the linear matrix inequalities-based and the variance-constrained ones. Finally, the effectiveness of the theoretical results is verified by a numerical simulation.

Performance of DCSK Cooperative Communication Systems Over Multipath Fading Channels

A differential chaos shift keying cooperative communication (DCSK-CC) system with two users is proposed in this paper, which has an orthogonal subchannel in broadcast phase and cooperative phase through orthogonal Walsh code sequences as its multiaccess scheme. The single relay cooperative network with decode-and-forward relay is investigated in the proposed system according to two cooperation protocols, namely, conventional cooperation and space-time cooperation. Unlike conventional CDMA cooperative communication (CDMA-CC) systems, quite surprisingly power control devices that consume more energy to mitigate near-far effects can be avoided in the proposed system, which is of great importance to energy-constrained networks such as wireless sensor networks. Simulation results demonstrate that, through a conventional cooperation mechanism, the proposed system has a prominent advantage of good bit-error-probability (BEP) performance over the CDMA-CC systems that have a single path correlation receiver, at the same data rate with a high SNR range over multipath Rayleigh fading channels. Meanwhile, it is found that conventional cooperation is a better cooperation strategy relative to space-time cooperation in the proposed system. In addition, a lower bound of BEP performance is derived and verified by simulations over independent three-ray Rayleigh fading channels.

Higher-Order Synchronization of Complex Dynamical Networks

Privacy Preserving via Secure Summation in Distributed Kalman Filtering

Average consensus is a major operation in distributed Kalman filtering. It requires neighboring nodes to exchange state information with each other, which may result in undesirable private data leakage. Since distributed Kalman filtering requires that the estimate at each time instant is accurate, it brings more challenges to design privacy-preserving scheme for operation. In this article, we design a privacy-preserving scheme for distributed Kalman filtering without the loss of estimation performance, which is also suitable for average consensus or dynamic average consensus of multiagent systems. We first build a secure multihop communication based on an encryption scheme. We then calculate the sum of the states of neighboring nodes with secure summation, which ensures that the state update will not reveal the state of the node to its neighboring nodes. We employ different methods to calculate the sum of the states of neighboring nodes against noncollusive and collusive adversaries. For the noncollusive case, the privacy of the honest nodes is preserved. For the collusive case, if there are too many adversaries, the privacy of the honest nodes could be exposed when accurate distributed Kalman filtering is accomplished. Therefore, we measure the risk of the global system suffering privacy leakage as the privacy index and improve the ability of the system to defend the collusive adversaries by using a group-based method. Some numerical examples are provided to illustrate the effectiveness of the proposed schemes.

Signal clustering of power disturbance by using chaos synchronization

This study develops and applies a chaos synchronization-based detection method for an engineering application of monitoring power quality disturbance. The new method can detect minor dynamic changes in signals. Likewise, prominent characteristics of system signal disturbance can be extracted by this technique. The method is then combined with the extension recognition algorithm to accurately apply to signal clustering of power disturbance. According to extensive computer simulation results and a comparison among three typical chaotic systems, it is confirmed that the proposed method is well applicable using various chaotic systems, mostly with very high accuracies. As compared with other traditional methods, the new method is shown to have higher accuracy, faster computing speed and better expandability. It is foreseen that if the method can be implemented by system-on-chip in the near future, it will find many real engineering applications such as hand-held power quality analyzers and auxiliary means for on-line real-time detection, among others.

Sequential Fusion Estimation for Renewable Energy Microgrids Under Hybrid Attacks: Handling Filter-and-Forward Relays

This artcle investigates the fusion estimation problem for renewable energy microgrids subject to relay transmissions and cyber-attacks. A filter-and-forward (FaF) relay strategy is adopted to ensure the reliable transmission of power signals from distributed sensors to the remote estimator. This strategy jointly accounts for both sensor-relay and relay-estimator channels when determining signal transmission, and relays with embedded filtering capabilities are considered essential for extracting relay signals from corrupted measurements. In addition, four stochastic sequences governed by Bernoulli distributions are employed to characterize denial-of-service and false data injection attacks, which occur randomly throughout the communication process. The principal objective is to improve estimation accuracy by constructing an estimation scheme capable of operating under the presence of FaF relays and hybrid attacks. Specifically, the proposed scheme consists of two main components: first, the design of a recursive filtering algorithm at each FaF relay for generating the relay signal, and second, the development of a sequential fusion estimation algorithm to enable accurate state estimation. Sufficient conditions are derived to guarantee the mean-square boundedness of both the filtering error and the estimation error. The effectiveness of the proposed estimation methodology is demonstrated through simulation experiments conducted on renewable energy microgrids in a wireless multisensor system.