Circulant matrix families have become an important tool in network engineering. In this paper, two new patterned matrices over ${\mathbb{Z}}_p$ which include row skew first-plus-last right circulant matrix and row first-plus-last left circulant matrix are presented. Their basic properties are discussed. Based on Newton-Hensel lifting and Chinese remaindering, two different algorithms are obtained. Moreover, the cost in terms of bit operations for each algorithm is given.

Recently many chaotic systems’ circuits are designed to generate phenomenon of chaos signals. The ability to synchronize chaotic circuits opens a great number of ways to use them in application signals masking. In this paper, first a new nonlinear chaotic dynamical system had be design, analyze and build circuit. Second, using GYC, partial region stability theory is applied to adaptive control for two identical chaotic systems with uncertain parameters. The results of numerical simulation are performed to verify examples of the proposed nonlinear controllers.

The current electric gas pressure regulator often adopts the conventional PID control algorithm to take drive control of the core part (micromotor) of electric gas pressure regulator. In order to further improve tracking performance and to shorten response time, this paper presents an improved PID intelligent control algorithm which applies to the electric gas pressure regulator. The algorithm uses the improved RBF neural network based on PSO algorithm to make online adjustment on PID parameters. Theoretical analysis and simulation result show that the algorithm shortens the step response time and improves tracking performance.

As platform based on users’ relationship to acquire, share, and propagate knowledge, Wechat develops very rapidly and becomes an important channel to spread knowledge. This new way to propagate knowledge is quite different from the traditional media way which enables knowledge to be spread surprisingly in Wechat. Based on complex network theory and the analysis of the factors which influence the knowledge propagation in Wechat, this paper summarizes the behavior preferences of Wechat users in knowledge propagation and establishes a Wechat knowledge propagation model. By the simulation experiment, this paper tests the model established and finds some important thresholds in knowledge propagation in Wechat. The findings are valuable for further studying the knowledge propagation in Wechat and provide theoretical proof for forecasting the scale and influence of knowledge propagation.

In recent years, theoretical and practical research topics on networked control systems (NCSs) have gained an increasing interest from many researchers in a variety of disciplines owing to the extensive applications of NCSs in practice. In particular, an urgent need has arisen to understand the effects of communication processes on system performances. Sampling and protocol are two fundamental aspects of a communication process which have attracted a great deal of research attention. Most research focus has been on the analysis and control of dynamical behaviors under certain sampling procedures and communication protocols. In this paper, we aim to survey some recent advances on the analysis and synthesis issues of NCSs with different sampling procedures (time- and event-driven sampling) and protocols (static and dynamic protocols). First, these sampling procedures and protocols are introduced in detail according to their engineering backgrounds as well as dynamic natures. Then, the developments of the stabilization, control, and filtering problems are systematically reviewed and discussed in great detail. Finally, we conclude the paper by outlining future research challenges for analysis and synthesis problems of NCSs with different communication processes.

This paper deals with the fault detection problem for a class of discrete-time wireless networked control systems described by switching topology with uncertainties and disturbances. System states of each individual node are affected not only by its own measurements, but also by other nodes’ measurements according to a certain network topology. As the topology of system can be switched in a stochastic way, we aim to design $H_{\infty }$ fault detection observers for nodes in the dynamic time-delay systems. By using the Lyapunov method and stochastic analysis techniques, sufficient conditions are acquired to guarantee the existence of the filters satisfying the $H_{\infty }$ performance constraint, and observer gains are derived by solving linear matrix inequalities. Finally, an illustrated example is provided to verify the effectiveness of the theoretical results.

This paper is concerned with the problem of the nonlinear dynamic surface control (DSC) of chaos based on the minimum weights of RBF neural network for the permanent magnet synchronous motor system (PMSM) wherein the unknown parameters, disturbances, and chaos are presented. RBF neural network is used to approximate the nonlinearities and an adaptive law is employed to estimate unknown parameters. Then, a simple and effective controller is designed by introducing dynamic surface control technique on the basis of first-order filters. Asymptotically tracking stability in the sense of uniformly ultimate boundedness is achieved in a short time. Finally, the performance of the proposed controller is testified through simulation results.

Circulant and skew circulant matrices have become an important tool in networks engineering. In this paper, we consider skew circulant type matrices with any continuous Fibonacci numbers. We discuss the invertibility of the skew circulant type matrices and present explicit determinants and inverse matrices of them by constructing the transformation matrices. Furthermore, the maximum column sum matrix norm, the spectral norm, the Euclidean (or Frobenius) norm, and the maximum row sum matrix norm and bounds for the spread of these matrices are given, respectively.

This paper addresses the finite-time synchronizing problem for a class of chaotic neural networks. In a real communication network, parameters of the master system may be time-varying and the system may be perturbed by external disturbances. A simple high-gain observer is designed to track all the nonlinearities, unknown system functions, and disturbances. Then, a dynamic active compensatory controller is proposed and by using the singular perturbation theory, the control method can guarantee the finite-time stability of the error system between the master system and the slave system. Finally, two illustrative examples are provided to show the effectiveness and applicability of the proposed scheme.

Some research on the stability with mode constraint for a class of infinite dimensional look-ahead interconnected systems with impulsive and stochastic disturbances is studied by using the vector Lyapunov function approach. Intuitively, the stability with mode constraint is the property of damping disturbance propagation. Firstly, we derive a set of sufficient conditions to assure the stability with mode constraint for a class of general infinite dimensional look-ahead interconnected systems with impulsive and stochastic disturbances. The obtained conditions are less conservative than the existing ones. Secondly, the controller for a class of look-ahead vehicle following systems with the above uncertainties is constructed by the sliding mode control method. Based on the obtained new stability conditions, the domain of the control parameters of the systems is proposed. Finally, a numerical example with simulations is given to show the effectiveness and correctness of the obtained results.

Nowadays, the real-world systems are usually subject to various complexities such as parameter uncertainties, time-delays, and nonlinear disturbances. For networked systems, especially large-scale systems such as multiagent systems and systems over sensor networks, the complexities are inevitably enhanced in terms of their degrees or intensities because of the usage of the communication networks. Therefore, it would be interesting to (1) examine how this kind of network-enhanced complexities affects the control or filtering performance; and (2) develop some suitable approaches for controller/filter design problems. In this paper, we aim to survey some recent advances on the performance analysis and synthesis with three sorts of fashionable network-enhanced complexities, namely, fading measurements, event-triggered mechanisms, and attack behaviors of adversaries. First, these three kinds of complexities are introduced in detail according to their engineering backgrounds, dynamical characteristic, and modelling techniques. Then, the developments of the performance analysis and synthesis issues for various networked systems are systematically reviewed. Furthermore, some challenges are illustrated by using a thorough literature review and some possible future research directions are highlighted.

As a kind of novel feedforward neural network with single hidden layer, ELM (extreme learning machine) neural networks are studied for the identification and control of nonlinear dynamic systems. The property of simple structure and fast convergence of ELM can be shown clearly. In this paper, we are interested in adaptive control of nonlinear dynamic plants by using OS-ELM (online sequential extreme learning machine) neural networks. Based on data scope division, the problem that training process of ELM neural network is sensitive to the initial training data is also solved. According to the output range of the controlled plant, the data corresponding to this range will be used to initialize ELM. Furthermore, due to the drawback of conventional adaptive control, when the OS-ELM neural network is used for adaptive control of the system with jumping parameters, the topological structure of the neural network can be adjusted dynamically by using multiple model switching strategy, and an MMAC (multiple model adaptive control) will be used to improve the control performance. Simulation results are included to complement the theoretical results.

This paper proposes an observer-based robust guaranteed cost control method for thrust-limited rendezvous in near-circular orbits. Treating the noncircularity of the target orbit as a parametric uncertainty, a linearized motion model derived from the two-body problem is adopted as the controlled plant. Based on this model, a robust guaranteed cost observer-controller is synthesized with a less conservative saturation control law, and sufficient condition for the existence of this observer-based rendezvous controller is derived. Finally, an illustrative example with immeasurable velocity states is presented to demonstrate the advantages and effectiveness of the control scheme.

This paper investigates the problem of stabilization of nonlinear discrete-time networked control systems (NCSs) with event-triggering communication scheme in the presence of signal transmission delay. A Takagi-Sugeno (T-S) fuzzy model and parallel-distributed compensation (PDC) scheme are first employed to design a nonlinear fuzzy event-triggered controller for the stabilization of nonlinear discrete-time NCSs. The idea of the event-triggering communication scheme (i.e., a soft computation algorithm) under consideration is that the current sensor data is transmitted only when the current sensor data and the previously transmitted one satisfy a certain state-dependent trigger condition. By taking the signal transmission delay into consideration and using delay system approach, a T-S fuzzy delay system model is established to describe the nonlinear discrete-time NCSs with event-triggering communication scheme. Attention is focused on the design of fuzzy event-triggered controller which ensures asymptotic stability of the closed-loop fuzzy systems. Linear matrix inequality- (LMI-) based conditions are formulated for the existence of admissible fuzzy event-triggered controller. If these conditions are feasible, a desired fuzzy event-triggered controller can be readily constructed. A nonlinear mass-spring-damper mechanical system is presented to demonstrate the effectiveness of the proposed method.

The existence and exponential stability of periodic solutions for inertial type BAM Cohen-Grossberg neural networks are investigated. First, by properly choosing variable substitution, the system is transformed to first order differential equation. Second, some sufficient conditions that ensure the existence and exponential stability of periodic solutions for the system are obtained by constructing suitable Lyapunov functional and using differential mean value theorem and inequality technique. Finally, two examples are given to illustrate the effectiveness of the results.

The problem of projective synchronization of drive-response coupled dynamical network with delayed system nodes and multiple coupling time-varying delays is investigated. Some sufficient conditions are derived to ensure projective synchronization of drive-response coupled network under the impulsive controller by utilizing the stability analysis of the impulsive functional differential equation and comparison theory. Numerical simulations on coupled time delay Lorenz chaotic systems are exploited finally to illustrate the effectiveness of the obtained results.

This paper investigates the exponential synchronization between two nonlinearly coupled complex networks with time-varying delay dynamical nodes. Based on the Lyapunov stability theory, some criteria for the exponential synchronization are derived with adaptive control method. Moreover, the presented results here can also be applied to complex dynamical networks with single time delay case. Finally, numerical analysis and simulations for two nonlinearly coupled networks which are composed of the time-delayed Lorenz chaotic systems are given to demonstrate the effectiveness and feasibility of the proposed complex network synchronization scheme.

This paper addresses the global consensus of nonlinear multiagent systems with asymmetrically coupled identical agents. By employing a Lyapunov function and graph theory, a sufficient condition is presented for the global exponential consensus of the multiagent system. The analytical result shows that, for a weakly connected communication graph, the algebraic connectivity of a redefined symmetric matrix associated with the directed graph is used to evaluate the global consensus of the multiagent system with nonlinear dynamics under the common linear consensus protocol. The presented condition is quite simple and easily verified, which can be effectively used to design consensus protocols of various weighted and directed communications. A numerical simulation is also given to show the effectiveness of the analytical result.

Synchronization is the strongest form of collective phenomena in complex systems of interacting components. In this paper, the problem of cluster projective synchronization of complex networks with fractional-order nodes based on the fractional-order differential equation stability theory is investigated. Only the nodes in one community which have direct connections to the nodes in other communities are controlled. Some sufficient synchronization conditions are derived via pinning control. Numerical simulations are provided to show the effectiveness of the theoretical results.

We consider an inhomogeneous growing network with two types of vertices. The degree sequences of two different types of vertices are investigated, respectively. We not only prove that the asymptotical degree distribution of type $s$ for this process is power law with exponent $\mathrm{2}+\left(\left(\mathrm{1}+\delta \right)q_s+\beta \left(\mathrm{1}-q_s\right)\right)/\alpha q_s$, but also give the strong law of large numbers for degree sequences of two different types of vertices by using a different method instead of Azuma’s inequality. Then we determine asymptotically the joint probability distribution of degree for pairs of adjacent vertices with the same type and with different types, respectively.

This paper is devoted to investigating stability in mean of partial variables for coupled stochastic reaction-diffusion systems on networks (CSRDSNs). By transforming the integral of the trajectory with respect to spatial variables as the solution of the stochastic ordinary differential equations (SODE) and using Itô formula, we establish some novel stability principles for uniform stability in mean, asymptotic stability in mean, uniformly asymptotic stability in mean, and exponential stability in mean of partial variables for CSRDSNs. These stability principles have a close relation with the topology property of the network. We also provide a systematic method for constructing global Lyapunov function for these CSRDSNs by using graph theory. The new method can help to analyze the dynamics of complex networks. An example is presented to illustrate the effectiveness and efficiency of the obtained results.

The global dissipative and multipeakon dissipative behavior of the two-component Camassa-Holm shallow water system after wave breaking was studied in this paper. The underlying approach is based on a skillfully defined characteristic and a set of newly introduced variables which transform the original system into a Lagrangian semilinear system. It is the transformation, together with the associated properties, that allows for the continuity of the solution beyond collision time to be established, leading to a uniquely global dissipative solution, which constructs a semigroup, and the multipeakon dissipative solution.

In this paper, we continue our investigations on control and synchronization of the complex Lorenz systems by investigating impulsive control and synchronization. Nonlinear systems involving impulse effects, appear as a natural description of observed evolution phenomena of several real world problems; For example, many biological phenomena involving thresholds, bursting rhythm models in medicine and biology, optimal control models in economics, population dynamics and so forth do exhibit impulsive effects. Some new and more comprehensive criteria for global exponential stability and asymptotical stability of impulsively controlled complex Lorenz systems are established with varying impulsive intervals. The effectiveness of the proposed technique is verified through numerical simulations.

The complex-valued neural networks with unbounded time-varying delays are considered. By constructing appropriate Lyapunov-Krasovskii functionals, and employing the free weighting matrix method, several delay-dependent criteria for checking the global $\mu$-stability of the addressed complex-valued neural networks are established in linear matrix inequality (LMI), which can be checked numerically using the effective LMI toolbox in MATLAB. Two examples with simulations are given to show the effectiveness and less conservatism of the proposed criteria.

A recent research indicated that the corticocortical connectivity network of the cat possesses cluster structure and that each cluster in the network is scale-free and has a most connected hub. Motivated by that research, we slightly modify the network model and derive sufficient conditions for cluster synchronization of the modified network based on Lyapunov function method. The obtained results indicate that cluster synchronization can be induced by the hubs of the scale-free networks. In our opinion, the concept of hub-induced synchronization provides a better understanding of cluster synchronization in scale-free networks. Numerical examples are provided to demonstrate the effectiveness of the theoretical results.

The European option pricing problem with transaction costs is investigated for a risky asset price model with Lévy jump. By the aid of arbitrage pricing theory and the generalized Itô formula (which includes Poisson jump), the explicit solution to the risk asset price model is given. According to arbitrage-free principle, we first discretize the continuous-time model. Then, in each small time interval, the transaction costs are introduced. By using the $\mathrm{\Delta }$-hedging strategy, the explicit solutions of the European options pricing formula with transaction costs are given for the risky asset price model with Lévy jump.

This paper is concerned with the problem of designing disturbance observer for fractional order systems, of which the disturbance is in time series expansion. The stability of a special observer with the selected nonlinear weighted function and transient dynamics function is rigorously analyzed for slowly varying disturbance. In addition, the result is also extended to estimate slope forms disturbance and higher order disturbance of fractional order systems. The efficacy of the proposed method is validated through numerical examples.