A general stability criterion for congestion control with diverse communication delays

A unified duality model is proposed for describing the current Internet congestion control algorithms. Based on this model, the problem of the local asymptotic stability of the congestion control with heterogeneous propagation delays is formulated and solved. A general stability criterion is proved by using the stability theory for quasi-polynomials.     

具有反馈时延的TCP Vega s 拥塞控制算法的稳定性分析

将Internet拥塞控制算法看作一个复杂的动态非线性反馈系统，借助多变量频率域控制系统的广义Nyquist判据和时延微分方程的Pontryagin判据，研究了各通信回路时延相同和时延不同条件下Internet网络拥塞控制算法，得到了具有反馈时延的TCP Vegas拥塞控制算法在平衡点渐近稳定的多个判据。仿真结果说明了稳定性判据的有效性和实用性。     

具有通信时延的二阶多智能体系统有限时间一致性跟踪控制

针对具有通信时延的二阶多智能体系统的有限时间一致性控制问题,分别研究了具有固定拓扑和切换拓扑网络结构情形下的二阶多智能体系统的有限时间一致性。为使多智能体系统能在有限时间内可以达到一致,引入一致性控制增益矩阵并设计了相应的基于相对位置和相对速度的时延状态误差有限时间一致性控制算法,利用系统模型转换,泛函微分方程稳定性理论和有限时间Lyapunov稳定性定理得到了使系统在有限时间内达到一致跟踪的最大时延上界值。最后,仿真实验结果验证了所得理论的正确性和有效性。     

Improved delay-range-dependent stability criteria for linear systems with time-varying delays

This paper is concerned with the stability analysis of linear systems with time-varying delays in a given range. A new type of augmented Lyapunov functional is proposed which contains some triple-integral terms. In the proposed Lyapunov functional, the information on the lower bound of the delay is fully exploited. Some new stability criteria are derived in terms of linear matrix inequalities without introducing any free-weighting matrices. Numerical examples are given to illustrate the effectiveness of the proposed method.     

具有通信时延的网络拥塞控制算法稳定性研究

稳定性是网络传输协议的一个关键性问题,在传统的协议设计方法中,首先实现协议的算法,然后再来分析协议的稳定性,调节相应参数。对Internet网络拥塞控制算法的动力学特性进行研究,在考虑网络时延的基础上,提出了一种广义原始-对偶模型,并分析该模型在任意拓扑网络结构中的稳定性,进而根据理论分析结果来设计具有渐进稳定性的拥塞控制算法。同时,就算法的稳定性进行了理论分析和仿真,给出了判断该分布式算法稳定的定理和参数的选择范围。仿真结果表明该广义原始-对偶拥塞控制算法是渐进稳定的。     

无线环境下拥塞控制算法的改进及其稳定性分析

无线网络中数据传输的往返时间RTT(roundtrip time)比有线网络中的RTT大,这使得针对有线网络设计的以时延作为拥塞信号的拥塞控制对偶算法应用到无线网络中时,其稳态性能下降,无线网络的带宽不能得到充分利用.针对对偶算法进行了改进,以保证该算法在无线网络中的稳态性能不会降低;同时,就改进算法的稳定性进行了理论分析和仿真,给出了判断该分布式算法稳定的定理和参数的选择范围.     

Stability of the Internet congestion control with diverse delays

Based on the clockwise property of parameterized curves and the general Nyquist criterion of stability, a conjecture on the stability of the Internet congestion control algorithm with diverse propagation delays is proved. A more general stability criterion is also provided. The new criterion preserves the elegancy of the conjecture being decentralized and locally implemented: each end system needs knowledge only of its own round-trip delay, but enlarges the stability region of control gains and admissible communication delays.     

Stability of distributed congestion control with heterogeneousfeedback delays

We investigate how congestion control can achieve efficient usage of network resources in the presence of heterogeneous communication delays between network users and resources. To this end, we consider a fluid flow model of network behavior. We study the stability of the system's behavior under small perturbations around the target equilibrium point (local stability). We establish several criteria for stability of certain linear delay-differential equations, via a technique which essentially reduces the question to studying stability of ordinary differential equations. These results are then used to derive sufficient conditions for local stability of the network congestion control problem. The same issue has been studied by Johari et al. (2001), where the authors propose a conjecture according to which local stability can be ensured in a distributed way. The correctness of the conjecture was established by Johari et al., only in degenerate cases where feedback delays coincide. Our results show that a modified form of the conjecture holds true for arbitrary feedback delays     

异构通信网联车系统鲁棒协同自适应巡航控制

考虑异构通信下的不确定网联车系统协同自适应巡航控制(CACC)问题,提出一种网联车系统鲁棒协同自适应巡航控制器设计方法.采用伯努利随机过程和具有可变输入延迟的跟踪模型描述具有参数不确定性和丢包及时延的异构通信网联车系统.为降低CACC控制器设计的复杂性,采用分散输出反馈控制结构和线性矩阵不等式技术,求解不确定异构通信网联车系统的CACC控制器.进一步,利用时滞系统方法和频域分析,建立保证闭环系统稳定和网联车辆系统弦稳定结果.最后通过一组四车辆三信道的网联车辆系统的仿真实验验证所提方法的有效性.     

一种改进的拥塞控制算法

为控制网络拥塞,提出一种改进的随机早期检测（RED)算法——基于加权和的随机早期检测（WHS-RED）算法。算法的基本思想是利用网络中队列长度及其变化率的加权和,动态地控制网络丢包率。建立了数学模型,并给出了计算机仿真分析结果。实验证明改进算法减小了网络丢包率和带宽延迟,在维持网络稳定性和减小队列的波动性方面优于原RED算法。     

Containment control for second-order multi-agent systems with time-varying delays

This paper considers the containment control problem for second-order multi-agent systems with time-varying delays. Both the containment control problem with multiple stationary leaders and the problem with multiple dynamic leaders are investigated. Sufficient conditions on the communication digraph, the feedback gains, and the allowed upper bound of the delays to ensure containment control are given. In the case that the leaders are stationary, the Lyapunov–Razumikhin function method is used. In the case that the leaders are dynamic, the Lyapunov–Krasovskii functional method and the linear matrix inequality (LMI) method are jointly used. A novel discretized Lyapunov functional method is introduced to utilize the upper bound of the derivative of the delays no matter how large it is, which leads to a better result on the allowed upper bound of the delays to ensure containment control. Finally, numerical simulations are provided to illustrate the effectiveness of the obtained theoretical results.     

Accelerating average consensus by using the information of second-order neighbours with communication delays

This article investigates the problem of accelerating average consensus in undirected and connected networks. The protocol using the information of second-order neighbours with communication delays is proposed and the delay effects on stability and the convergence speed are analysed, respectively, under an assumption about the network topologies. It is proved that, for appropriate communication delays, networks reach average consensus faster under the proposed protocol than the standard protocol using only the information of first-order neighbours. Finally, a simulation example is presented to illustrate the proposed results.     

具有时变时滞耦合的二阶多主体系统的编队控制

多主体系统的编队控制是一类重要的网络协同控制问题.研究了在有向连接拓扑结构下,具有时变时滞耦合的二阶多主体系统的编队控制问题.通过一种多层领导机制的框架建模,得到了时不变编队、时变编队和时变轨迹追踪3种编队问题的充分性条件,并证明了各种预期队列是以指数的收敛速度形成的.数值仿真进一步验证了理论结果的正确性,为该理论在实际中应用起到指导作用.     

Stability analysis in a second-order differential equation with delays

A second-order differential equation with finite discrete delays is considered. Local stability of the zero equilibrium is investigated, and we obtain some sufficient conditions for the zero equilibrium is stable or unstable. Moreover, it is found that there exist the local Hopf bifurcations of the system when the delay varies.     

Event-based control with communication delays and packet losses

Event-based control aims at reducing the information exchange over the communication network in feedback-control systems. This article extends a state-feedback approach to event-based control to cope with communication delays and packet losses in the feedback link. The main result is a bound for the maximum tolerable communication delay, which guarantees that the event-based state-feedback loop is stable in the sense that its state remains in a bounded surrounding of the state of a continuous-time state-feedback loop. This result is extended to communication links with additional packet losses. Simulation studies and experimental results illustrate the performance of the event-based control loop.     

Asymptotic stability of congestion control systems with multiple sources

Congestion in computer networks is the main reason for reduced performance and poor quality of service; therefore, a good congestion control system is essential. The basic property of any control system is stability. We consider the problem of stability in computer network congestion control systems with multiple sources, which is the most common case in general purpose computer networks. The main result of the note is the proof that for congestion control systems with linear controllers (e.g., ATM-ABR), the stability of the congestion control system with a single source is equivalent to the stability of the one with multiple sources. In other words, for the considered congestion control systems, if the system is stable for a single source it will be stable for an arbitrary large number of sources. The proof is based on a well-known necessary and sufficient stability test.     

A delay partitioning approach to delay-range-dependent stability analysis of fuzzy systems

This paper is concerned with the stability analysis of Takagi-Sugeno (T-S) fuzzy systems with time varying delays in a given range. The delay partitioning approach is proposed to solving the problem of stability analysis for T-S fuzzy systems. By employing a new type of Lyapunov-Krasovskii functionals, delay-range-dependent stability criteria are derived for T-S fuzzy systems. The idea of the approach is that the delay interval is uniformly divided into N segments with N a positive integer, and a proper Lyapunov-Krasovskii functional is chosen with different weighted matrices corresponding to different segments in the Lyapunov-Krasovskii functional. All the sufficient criteria are established in terms of linear matrix inequalities (LMIs), which can be solved efficiently by using the LMI algorithm. Finally, numerical example is given to illustrate the less conservatism of the proposed method.     

Consensus of linear multi-agent systems with communication delays by using the information of second-order neighbours under intermittent communication topology

This paper investigates the consensus of identical linear multi-agent systems with aperiodic intermittent communication topology by using the information of second-order neighbours (two-hop neighbourhood). The protocols based on two-hop neighbourhood information and intermittent communication topology are designed, under which consensus is reached. If the communication rate is larger than the corresponding threshold value, the networks will accelerate consensus by using two-hop neighbourhood information. By means of switching systems theory and Lyapunov–Razumikhin theorem, consensus of multi-agent systems with communication delays and intermittent communication topology is reached by two-hop neighbourhood information. Finally, simulation examples are provided to show the effectiveness of the theoretical results.     

Formation control of multi-agent systems with heterogeneous communication delays

In this article, the formation control is investigated for a network of second-order dynamic agents with heterogeneous communication delays. The desired stationary formation is achieved by introducing diverse self-delay for each agent. In addition, a delay-dependent formation control algorithm is proposed to achieve the desired moving formation. Based on the frequency-domain analysis and matrix theory, sufficient conditions are obtained for the multi-agent systems asymptotically converging to desired stationary and moving formations, respectively. Simulation results illustrate the correctness of the results.     

Containment control of multi-agent systems with unbounded communication delays

In this paper, we address the containment control problem for multi-agent systems under heterogeneous unbounded communication delays with emphasis on the convergence rate analysis. Different from most works on multi-agent systems, we resort to a viewpoint from the area of positive delay systems. We first cast the containment control problem into the stability analysis of an associated error system. In order to capture the convergence rate, we introduce a nondecreasing positive function whose reciprocal represents the decay rate of the associated error system. Under the assumption that each follower has access to at least one leader and some mild hypotheses on the communication delays, an explicit condition is given to characterise the decay rate of the associated error system in terms of linear programming. In addition, we provide several special cases when the communication delays are restricted by linear, sublinear and logarithmic growth rates, respectively. Finally, through numerical examples, it is shown that the convergence rate is dominated by the delays being the highest order infinitely large quantity.