Publications

In this brief, a coordinated tracking control problem for a multi-agent system with noisy communication channels is considered under a leader–follower framework. Two control gain functions are designed, where the first one is used to attenuate the noise effect and the second is used to stabilize the system. Using tools from the algebraic graph theory and stochastic analysis, it is proved that, even over a switching directed network topology, the followers can track the leader in mean square.

This article investigates state estimation 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 mean-square estimation 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.

Without assuming that the communication topology can maintain its connectivity frequently enough during the evolution of agents, the flocking problem of multi-agent systems with second-order nonlinear dynamics is investigated in this paper. By combining the ideas of collective potential functions and velocity consensus, a connectivity-preserving flocking algorithm with bounded potential function is proposed. Using tools from algebraic graph theory and matrix analysis, it is shown that the present algorithm can enable the group of multiple agents to move with the same velocity while preserving the connectivity of the whole network if the the algebraic connectivity of the initial network is larger than a threshold value. Furthermore, the flocking algorithm is used to solve the flocking problem of multi-agent systems with a virtual leader by adding a navigation feedback term. In this case, each informed agent only has partial velocity information about the leader, yet the present algorithm not only can guarantee the velocity of the whole group to track that of the leader asymptotically, and also can preserve the connectivity of the network. Finally, simulation results are provided to valid the effectiveness of the theoretical results.

We adopt Gamma renewal process to describe the synaptic input of Hodgkin-Huxley neurons on a square lattice with no-flux boundary. Based on the eigenfunction expansion of Laplace operator, we show that the Hopf bifurcation point of the lattice is coincident with that of a single neuron model. By center manifold theorem and normal form theory, we prove that the Hopf bifurcation is subcritical. And then, we exhibit the effect of Gamma noise on the formation of spiral wave for the first time. It is revealed that the occurrence and elimination of the spiral wave can be controlled by adjusting the inhibitory-excitatory ratio and noise parameters. Since spiral waves may contribute to both normal cortical and pathological activities, the present investigation should be helpful for understanding the functional role of general neural noise.

Scientific Committee: Nicholas Alikakos, Peter Bates(Chair), Yongluo Cao, Guanrong Chen, Sui Sun Cheng, Shui-Nee Chow(Co-chair), L.O. Chua, Xilin Fu, Giorgio Fusco, Bolin Guo, Lihong Huang, Wenzhang Huang, Jifa Jiang, Christopher Jones, Tibor Krisztin, Chengzhi Li, Jia Li, Weigu Li, Yong Li, Xiao-Biao Lin, Bing Liu, Weishi Liu, Kening Lu, Zhien Ma, Dingbian Qian, Shigui Ruan, Wenxian Shen, Junping Shi, Yuefei Wang, Junjie Wei, Lan Wen, Jianhong Wu, Zhihong Xia, Dongmei Xiao, Daoyi Xu, Yuantong Xu, Xiangdong Ye, Yingfei Yi, Jiangong You, Rong Yuan, Xiaoping Yuan, Chongchun Zeng, Meirong Zhang, Weinian Zhang, Xiang Zhang, Xiaoqiang Zhao, Shengfan Zhou, Deming Zhu, Huaiping Zhu, Xingfu Zou

Dynamics of chaotic maps in an infinite-precision domain have been established complete mathematical framework. The case in finite-precision computer remains to be further explored. The related previous works treated a digital chaotic map as a black box and gave different explanations according to the test results of the output. Using the Logistic and Tent maps as typical examples, we disclose some dynamical properties of chaotic maps in fixed-point arithmetic by studying its corresponding state-mapping network (SMN), where every possible value is considered as a node and the mapping relation existing between any pair of nodes works as a directed edge. The scale-free properties of SMN are quantitatively proven. The obtained results can be extended to the scenario of floating-point arithmetic and to other chaotic maps. Understanding the real network structure of SMN of a chaotic map in the digital computer can facilitate counteracting dynamics degeneration of digital chaotic maps, which also help evaluate and improve the randomness of pseudo-random number sequences generated by iterating chaotic maps.

In this paper, we propose a susceptible-infected model with identical infectivity, in which, at every time step, each node can only contact a constant number of neighbors. We implemented this model on scale-free networks, and found that the infected population grows in an exponential form with the time scale proportional to the spreading rate. Furthermore, by numerical simulation, we demonstrated that the targeted immunization of the present model is much less efficient than that of the standard susceptible-infected model. Finally, we investigate a fast spreading strategy when only local information is available. Different from the extensively studied path-finding strategy, the strategy preferring small-degree nodes is more efficient than that preferring large-degree nodes. Our results indicate the existence of an essential relationship between network traffic and network epidemic on scale-free networks.

Controlling non-affine non-linear systems is a challenging problem in control theory. In this paper, we consider adaptive neural control of a completely non-affine pure-feedback system using radial basis function (RBF) neural networks (NN). An ISS-modular approach is presented by combining adaptive neural design with the backstepping method, input-to-state stability (ISS) analysis and the small-gain theorem. The difficulty in controlling the non-affine pure-feedback system is overcome by achieving the so-called “ISS-modularity” of the controller-estimator. Specifically, a neural controller is designed to achieve ISS for the state error subsystem with respect to the neural weight estimation errors, and a neural weight estimator is designed to achieve ISS for the weight estimation subsystem with respect to the system state errors. The stability of the entire closed-loop system is guaranteed by the small-gain theorem. The ISS-modular approach provides an effective way for controlling non-affine non-linear systems. Simulation studies are included to demonstrate the effectiveness of the proposed approach.