Zhuzhi Yuan

Brief paper: Reaching a consensus via pinning control

The consensus problem in a multi-agent system with general nonlinear coupling is investigated in this paper. It is demonstrated that, under suitable conditions on communication, all agents approach a prescribed value if a small fraction of them are controlled by simple feedback control. The stability analysis is based on a blend of graph-theoretic and system-theoretic tools where the contraction analysis and multiple Lyapunov functions play central roles. Numerous numerical examples, which support the analytical results very well, are also included.

New Chaotic PSO-Based Neural Network Predictive Control for Nonlinear Process

In this letter, a novel nonlinear neural network (NN) predictive control strategy based on the new tent-map chaotic particle swarm optimization (TCPSO) is presented. The TCPSO incorporating tent-map chaos, which can avoid trapping to local minima and improve the searching performance of standard particle swarm optimization (PSO), is applied to perform the nonlinear optimization to enhance the convergence and accuracy. Numerical simulations of two benchmark functions are used to test the performance of TCPSO. Furthermore, simulation on a nonlinear plant is given to illustrate the effectiveness of the proposed control scheme

A HYPERCHAOS GENERATED FROM CHEN'S SYSTEM

This paper presents a new hyperchaotic system, obtained by adding a controller to the second equation of the three-dimensional autonomous Chens chaotic system. The hyper-chaos system undergoes a change from hyperchaos to limit cycle when the parameter varies. The system is not only demonstrated by computer simulations but also verified with bifurcation analysis.

Event-triggered average-consensus of multi-agent systems with weighted and direct topology

This paper investigates the average-consensus problem of multi-agent systems with direct and weighted topologies. Event-triggered control laws are adopted so as to reduce the frequency of individual control updating since the agents may be resource-limited in many real systems. The discrete time instants where the events are triggered are determined by a trigger function with respect to a certain measurement error. A centralized average-consensus protocol is proposed first for networks with fixed interaction topology, the stability and influencing factors of which are also analyzed. The design of trigger functions for networks with variable topology is also discussed. Then the results are extended to the decentralized counterpart, in which agents require only the information of their neighbors. Numerical examples are also provided that demonstrate the effectiveness of the theoretical results.

Chaotifying linear Elman networks

A linear model of recurrent neural networks, called the Elman networks, is combined with the simple nonlinear modulo (mod) operation on its linear activated function so as to generate chaos purposely. Conditions on the weight matrix are obtained, under which the generated chaos satisfies the mathematical definition of chaos in the sense of T.Y. Li and J.A. Yorke (1975). Some simple and representative weight matrices are constructed for designing such Elman networks that can generate Li-Yorke chaos. Several numerical simulations are shown to verify and visualize the design.

A NOVEL HYPERCHAOTIC SYSTEM AND ITS COMPLEX DYNAMICS

This paper is concerned with a novel four-dimensional continuous autonomous hyperchaotic system, which is obtained by adding a simple dynamical state-feedback controller to a Lorenz-like three-dimensional autonomous chaotic system. This new system contains three parameters and each equation of the system has one quadratic cross-product term. Some basic properties of the system are studied first. Its complex dynamic behaviors are then analyzed by means of Lyapunov exponent (LE) spectrum, bifurcation diagrams, phase portraits and Poincare sections. It is shown that the system has several large hyperchaotic regions. When the system is evolving in a hyperchaotic region, the two positive LEs are both large, which can be larger than 1 if the system parameters are taken appropriately. The pitchfork bifurcation of the system is finally analyzed by using the center manifold theorem.

Pinning control of complex dynamical networks with heterogeneous delays

Complex dynamical networks with heterogeneous delays in both continuous- and discrete-time domains are controlled by applying local feedback injections to a small fraction of nodes in the whole network. Some generic stability criteria ensuring delay-independent stability are derived for such controlled networks in terms of linear matrix inequalities (LMI), which guarantee that by placing a small number of feedback controllers on some nodes, the whole network can be pinned to its equilibrium. In some particular cases, a single controller can achieve the control objective. Numerical simulations of various representative networks, including a globally coupled network, a star-coupled network and an Extended Barabasi-Albert (EBA) scale-free network, are finally given for illustration and verification.

Pinning weighted complex networks with heterogeneous delays by a small number of feedback controllers

Weighted complex dynamical networks with heterogeneous delays in both continuous-time and discrete-time domains are controlled by applying local feedback injections to a small fraction of network nodes. Some generic stability criteria ensuring delay-independent stability are derived for such controlled networks in terms of linear matrix inequalities (LMIs), which guarantee that by placing a small number of feedback controllers on some nodes the whole network can be pinned to some desired homogeneous states. In some particular cases, a single controller can achieve the control objective. It is found that stabilization of such pinned networks is completely determined by the dynamics of the individual uncoupled node, the overall coupling strength, the inner-coupling matrix, and the smallest eigenvalue of the coupling and control matrix. Numerical simulations of a weighted network composing of a 3-dimensional nonlinear system are finally given for illustration and verification.

EPIDEMICS OF SIRS MODEL WITH NONUNIFORM TRANSMISSION ON SCALE-FREE NETWORKS

We investigate the effect of nonuniform transmission on the critical threshold of susceptible–infected–recovered–susceptible (SIRS) epidemic model on scale-free networks. Based on the mean-field theory, it is observed that the epidemic threshold is not only correlated with the topology of underlying networks, but also with the disease transmission mechanism (e.g., nonuniform transmission). The current findings will significantly help us to further understand the real epidemics taking place on social and technological networks.

Generating chaos by an Elman network

A new nonlinear neuron-activation function is introduced into the framework of an Elman network, thereby enabling the neural network to generate chaos. Basic analysis of its fixed point stability and parameter selection criterion for chaos generation is given, and is verified via simulation studies.