Average consensus of multi-agent systems with communication time delays and noisy links

In this paper,we consider the average-consensus problem with communication time delays and noisy links.We analyze two different cases of coupling topologies：fixed and switching topologies.By utilizing the stability theory of the stochastic differential equations,we analytically show that the average consensus could be achieved almost surely with the perturbation of noise and the communication time delays even if the time delay is time-varying.The theoretical results show that multi-agent systems can tolerate relatively large time delays if the noise is weak,and they can tolerate relatively strong noise if the time delays are low.The simulation results show that systems with strong noise intensities yield slow convergence.

Sufficient Condition for Average Consensus of Directed Networked Multi-agent Systems with Time Delays

The average consensus problem in a directed network of multi-agent systems with communication time delays was investigated. The directed networks were balanced and weakly connected with fixed or switching topology digraph. Based on frequency domain analysis method, a sufficient condition of asymptotic stability of multi-agent systems with time delays was obtained,where the analytic formula between the maximum time delay and the directed network structure was provided. The maximum time delay can be derived directly and easily by the eigenvalue of Laplacian L. Numerical examples confirm the effectiveness of the proposed technique.

Average Consensus in Networks of Multi-Agent with Multiple Time-Varying Delays

The average consensus in undirected networks of multi-agent with both fixed and switching topology coupling multiple time-varying delays is studied. By using orthogonal transformation techniques, the original system can be turned into a reduced dimensional system and then LMI-based method can be applied conveniently. Convergence analysis is conducted by constructing Lyapunov-Krasovskii function. Sufficient conditions on average consensus problem with multiple time-varying delays in undirected networks are obtained via linear matrix inequality (LMI) techniques. In particular, the maximal admissible upper bound of time-varying delays can be easily obtained by solving several simple and feasible LMIs. Finally, simulation examples are given to demonstrate the effectiveness of the theoretical results.

A modified averaging scheme with application to the secondary Hopf bifurcation of a delayed van der Pol oscillator

In this paper, a modified averaging scheme is presented for a class of time-delayed vibration systems with slow variables. The new scheme is a combination of the averaging techniques proposed by Hale and by Lehman and Weibel, respectively. The averaged equation obtained from the modified scheme is simple enough but it retains the required information for the local nonlinear dynamics around an equilibrium. As an application of the present method, the delay value for which a secondary Hopf bifurcation occurs is successfully located for a delayed van der Pol oscillator.

Internet end-to-end delay dynamics

End-to-end delay is one of the most important characteristics of Internet end-to-end packet dynamics, which can be applied to quality of services （OoS） management, service level agreement （SLA） management, congestion control algorithm development, etc. Nonstationarity and nonlinearity are found by the analysis of various delay series measured from different links. The fact that different types of links have different degree of Self-Similarity is also obtained. By constructing appropriate network architecture and neural functions, functional networks can be used to model the Internet end-to-end nonlinear delay time series. Furthermore, by using adaptive parameter studying algorithm, the nonstationarity can also be well modeled. The numerical results show that the provided functional network architecture and adaptive algorithm can precisely characterize the Internet end-to-end delay dynamics.

AN AVERAGING PRINCIPLE FOR STOCHASTIC DIFFERENTIAL DELAY EQUATIONS DRIVEN BY TIME-CHANGED LéVY NOISE

In this paper,we aim to derive an averaging principle for stochastic differential equations driven by time-changed Lévy noise with variable delays.Under certain assumptions,we show that the solutions of stochastic differential equations with time-changed Lévy noise can be approximated by solutions of the associated averaged stochastic differential equations in mean square convergence and in convergence in probability,respectively.The convergence order is also estimated in terms of noise intensity.Finally,an example with numerical simulation is given to illustrate the theoretical result.

Research on Network Delays of Networked Control Systems

In networked control systems (NCS), the main problem is time delays induced by communication network, which can deteriorate the performance of the systems, even cause the systems instability. If we know the exact network delays, we can compensate for their effect by modifying the parameters of the controller. Hence how to get the knowledge of these delays in the network is critical. This paper analyzed the different characteristics of network delays from sensor to controller and from controller to actuator and presented the methods of online evaluation of these delays. The experiment shows these methods are valid.

ADMM-based Distributed Algorithm for Economic Dispatch in Power Systems With Both Packet Drops and Communication Delays

By virtue of alternating direction method of multipliers(ADMM), Newton-Raphson method, ratio consensus approach and running sum method, two distributed iterative strategies are presented in this paper to address the economic dispatch problem(EDP) in power systems. Different from most of the existing distributed ED approaches which neglect the effects of packet drops or/and time delays, this paper takes into account both packet drops and time delays which frequently occur in communication networks. Moreover, directed and possibly unbalanced graphs are considered in our algorithms, over which many distributed approaches fail to converge. Furthermore, the proposed schemes can address the EDP with local constraints of generators and nonquadratic convex cost functions, not just quadratic ones required in some existing ED approaches. Both theoretical analyses and simulation studies are provided to demonstrate the effectiveness of the proposed schemes.

A PCA-Based Internet Delay Space Dividing Algorithm

It's a hot issue to improve the accuracy of network coordinate systems(NCS). By analyzing the error source of NCSes, it's emphasized that guaranteeing the low dimensionality of embedding datasets is the principle on the designing of NCSes. Based on this observation, a PCA based Internet delay space dividing algorithm(IDSD-PCA) is proposed. Beginning at choosing an optimized sub dataset randomly, IDSD-PCA partitions the Internet delay dataset into several sub datasets with low dimensionality by iterations. After the partition, the whole delay dataset and sub datasets are embedded into a hierarchical NCS. The experimental results show that with this framework both the metric space based models and the non-metric space based models can predict the end-to-end delays more accurately.

Robust exponential stability of uncertain discretetime impulsive switching systems with state delay

A new class of hybrid impulsive and switching models are introduced and their robust exponential stability and control synthesis are addressed. The proposed switched system is composed of stable subsystems and unstable subsystems, which not only involves state delay and norm-bounded time-varying parameter uncertainties, but also contains the impulsive switching effects between the subsystems. Based on the extension of the system dimension and the concept of average dwell time, a kind of practically useful switching rule is presented which guarantees the desired robust exponential stability. A switched state feedback controller is also given.

Input-to-State Stabilization of Nonlinear Impulsive Delayed Systems: An Observer-Based Control Approach

This paper addresses the problems of input-to-state stabilization and integral input-to-state stabilization for a class of nonlinear impulsive delayed systems subject to exogenous dis-turbances.Since the information of plant’s states,time delays,and exogenous disturbances is often hard to be obtained,the key design challenge,which we resolve,is the construction of a state observer-based controller.For this purpose,we firstly propose a corresponding observer which is independent of time delays and exogenous disturbances to reconstruct(or estimate)the plant’s states.And then based on the observations,we establish an observer-based control design for the plant to achieve the input-to-state stability(ISS)and integral-ISS(iISS)properties.With the help of the comparison principle and average impulse interval approach,some sufficient conditions are presented,and moreover,two different linear matrix inequalities(LMIs)based criteria are proposed to design the gain matrices.Finally,two numerical examples and their simulations are given to show the effectiveness of our theoretical results.

Some generalized limit theorems concerning delayed sums of random sequence

For a sequence of arbitrarily dependent m-valued random variables （Xn） n∈N , the generalized strong limit theorem of the delayed average is investigated. In our proof, we improved the method proposed by Liu [6] . As an application, we also studied some limit properties of delayed average for inhomogeneous Markov chains.

Analysis of a Delayed Stochastic One-Predator Two-Prey Population Model in a Polluted Environment

This paper is concerned with the dynamics of a delayed stochastic one-predator two-prey population model in a polluted environment. We show that there exists a unique positive solution that is permanent in time average under certain conditions. Moreover, the global attractively of system is studied. Finally, some numerical simulations are given to illustrate the main results.

H_-/H_∞ fault detection filter design for interval time-varying delays switched systems

The problem of the robust fault detection filter design for time-varying delays switched systems is considered in the framework of mixed H-/H∞. Firstly, the weighted H∞ performance index is utilized as the robustness performance, and the H- index is used as the sensitivity performance for obtaining the robust fault detection filter. Then a novel multiple Lyapunov-Krasovskii function is proposed for deriving sufficient existence conditions of the robust fault detection filter based on the average dwell time technique. By introducing slack matrix variable, the coupling between the Lyapunov matrix and system matrix is removed, and the conservatism of results is reduced. Based on the robust fault detection filter, residual is generated and evaluated for detecting faults. In addition, the results of this paper are dependent on time delays,and represented in the form of linear matrix inequalities. Finally,the simulation example verifies the effectiveness of the proposed method.

Online Delay-Evaluation Approach in Networked Control Systems

This paper presents an online evaluation approach of time delays for networked control systems (NCS), which characterizes the time delays without any synchronized clock in the network and any assumptions of time delays. With this approach, an optimal control scheme based on the approach is designed to achieve the desired performance despite the uncertain delays in the system. The experimental results based on CANbus illustrate the effectiveness of the proposed control design and satisfactory performance of the closed-loop system.

A statistical end-to-end performance model for networks with complex topologies

Network calculus provides new tools for performance analysis of networks, but analyzing networks with complex topologies is a challenging research issue using statistical network calculus. A service model is proposed to characterize a service process of network with complex topologies. To obtain closed-form expression of statistical end-to-end performance bounds for a wide range of traffic source models, the traffic model and service model are expanded according to error function. Based on the proposed models, the explicit end-to-end delay bound of Fractional Brownian Motion（FBM） traffic is derived, the factors that affect the delay bound are analyzed, and a comparison between theoretical and simulation results is performed. The results illustrate that the proposed models not only fit the network behaviors well, but also facilitate the network performance analysis.

Mean Square Average Generalized Consensus of Multi-Agent Systems Under Time-Delays and Stochastic Disturbances

Compared with the traditional consensus problem, this paper deals with the mean square average generalized consensus(MSAGC) of multi-agent systems under fixed directed topology, where all agents are affected by stochastic disturbances. Distributed protocol depending on delayed time information from neighbors is designed. Based on Lyapunov stability theory, together with results from matrix theory and It o s derivation theory, the linear matrix inequalities approach is used to establish sufficient conditions to ensure MSAGC of multi-agent systems. Finally, numerical simulations are provided to illustrate the theoretical results.

Research on service capacity of widened intersection based on traffic simulation

Delay analysis method is adopted to study the service capacity of a widened intersection. Traffic simulation software VISSIM is used for microscopic simulation of a widened intersection so as to obtain a delay curve. The delay-volume model of a widened intersection is established based on traffic simulation. The suggested value of basic service capacity of the widened left-turn lane is given along with how to determine correction factors and practical service capacity.

Stochastic averaging technique for SDOF strongly nonlinear systems with delayed feedback fractional-order PD controller

A stochastic averaging technique is proposed to study the randomly excited single-degree-of-freedom(SDOF) strongly nonlinear systems with delayed feedback fractional-order proportional-derivative(PD) controller. The delayed feedback fractional-order PD control force is approximated by an equivalent non-delay feedback control force combining with a quasi-linear elastic force and a quasi-linear damping force. The averaged It? stochastic differential equation for amplitude of the equivalent nonlinear system is derived by the generalized harmonic functions. The analytical stationary probability density function(PDF) is obtained with solving the reduced Fokker-Planck-Kolmogorov(FPK) equation. Two examples of van der Pol oscillator and RayleighDuffing oscillator are studied to illustrate the application and effectiveness of the proposed method. Numerical results display that the proposed method can yield to the high precision, and the time delay could ruin the control effectiveness, but also even amplifies the response of the system more than that of uncontrolled system. Furthermore, the study finds that the parameters of fractional-order α and time delay may cause the stochastic P-bifurcation. It is indicated that the delayed feedback fractional-order PD controller can offer a potentially effective tool for anti-control of stochastic bifurcation

Real-time Performance Evaluation of Line Topology Switched Ethernet

Recently,switched Ethernet has become an active area of research because of its wide uses in industry.However,its uses have various real-time constraints on data communications.This paper analyzes the performance of the line topology switched Ethernet as a data acquisition network.Network calculus theory,which has been successfully applied to assess the real-time performance of packet-switched networks,is used to analyze the networks.To properly describe the activity of switches,a novel approach of modeling data flows into or out of switches is addressed.Based on our model,a concisely analytical expression of the maximal end-to-end delay in line topology switched Ethernet is derived.Finally,the relative simulation results are demonstrated.These results agree well with the analytical results,and thus they validate the data flow modeling techniques.