Robust stability analysis of Smith predictor-based congestion control algorithms for computer networks

Congestion control is a fundamental building block in packet switching networks such as the Internet due to the fact that communication resources are shared. It has been shown that the plant dynamics is essentially made up of an integrator plus time delay and that a proportional controller plus a Smith predictor defines a simple and effective controller. It has also been shown that the TCP congestion control can be modelled using a Smith predictor plus a proportional controller. Due to the importance of this control structure in the field of data network congestion control, we analyse the robust stability of the closed-loop system in the face of delay uncertainties that are present in data networks due to queuing. In particular, by applying a geometric approach, we derive a bound on the proportional controller gain which is necessary and sufficient to guarantee the closed-loop stability for a given bound on the delay uncertainty.     

无线接入网中一类联合调度算法的鲁棒稳定性分析

针对无线通讯中的随机时延抖动和外界干扰等会引发数据包传输的不稳定问题,研究不稳定传输下无线接入网中一类联合调度算法的鲁棒稳定性.首先,通过将基站中的队列尺寸定义为系统状态,并将不稳定传输建模为分布函数未知的随机扰动,利用具有一个弹性壁的Markov随机游走模型描述系统状态的变化;其次,根据在联合调度算法下系统状态的期望逗留时间等信息,得到该Markov模型的状态转移概率矩阵;再次,给出模型中状态正常返的充分条件,即队列尺寸的鲁棒稳定性判据,并对该判据进行验证;最后,通过数值仿真结果表明了所提方法的有效性.     

Robust stability and performance analysis for linear dynamicsystems

In a recent paper K. Zhou and P.P. Khargonekar (ibid., vol.AC-32, pp.621-623, 1987) obtained sufficient conditions for robust stability over specified sets of matrix perturbations. These results are here extended to include performance bounds. Performance is defined as the worst-case expected value of a quadratic functional involving the state variables when the system is subjected to white noise disturbances. The results are illustrated by considering the gain margin of both an LQG controller and a robustified design obtained by D.S. Bernstein and S.W. Greeley (1986) for J.C. Doyle's examples     

Robust stability analysis of robot control systems

Some robust stability measures for state-space models are discussed. These measures are used for assessing the robustness of a robotic system controlled by a form of the PID control algorithm. The highly nonlinear and strongly coupled robot model is replaced by a nominal linear model involving modelling uncertainty. The amount of uncertainty under which the robotic system can maintain its stability and tracking performance is determined using the above measures. The parametric sensitivity of the robotic system is also briefly considered.     

Robust domain adaptation

We derive a generalization bound for domain adaptation by using the properties of robust algorithms. Our new bound depends on λ-shift, a measure of prior knowledge regarding the similarity of source and target domain distributions. Based on the generalization bound, we design SVM variants for binary classification and regression domain adaptation algorithms.     

Robust adaptive algorithms for underwater acoustic channel estimation and their performance analysis

We introduce a novel family of adaptive robust channel estimators for highly challenging underwater acoustic (UWA) channels. Since the underwater environment is highly non-stationary and subjected to impulsive noise, we use adaptive filtering techniques based on minimization of a logarithmic cost function, which results in a better trade-off between the convergence rate and the steady state performance of the algorithm. To improve the convergence performance of the conventional first and second order linear estimation methods while mitigating the stability issues related to impulsive noise, we intrinsically combine different norms of the error in the cost function using a logarithmic term. Hence, we achieve a comparable convergence rate to the faster algorithms, while significantly enhancing the stability against impulsive noise in such an adverse communication medium. Furthermore, we provide a thorough analysis for the tracking and steady-state performances of our proposed methods in the presence of impulsive noise. In our analysis, we not only consider the impulsive noise, but also take into account the frequency and phase offsets commonly experienced in real life experiments. We demonstrate the performance of our algorithms through highly realistic experiments performed on accurately simulated underwater acoustic channels.     

Randomized algorithms for stability and robustness analysis of high-speed communication networks

This paper initiates a study toward developing and applying randomized algorithms for stability of high-speed communication networks. The focus is on congestion and delay-based flow controllers for sources, which are "utility maximizers" for individual users. First, we introduce a nonlinear algorithm for such source flow controllers, which uses as feedback aggregate congestion and delay information from bottleneck nodes of the network, and depends on a number of parameters, among which are link capacities, user preference for utility, and pricing. We then linearize this nonlinear model around its unique equilibrium point and perform a robustness analysis for a special symmetric case with a single bottleneck node. The "symmetry" here captures the scenario when certain utility and pricing parameters are the same across all active users, for which we derive closed-form necessary and sufficient conditions for stability and robustness under parameter variations. In addition, the ranges of values for the utility and pricing parameters for which stability is guaranteed are computed exactly. These results also admit counterparts for the case when the pricing parameters vary across users, but the utility parameter values are still the same. In the general nonsymmetric case, when closed-form derivation is not possible, we construct specific randomized algorithms which provide a probabilistic estimate of the local stability of the network. In particular, we use Monte Carlo as well as quasi-Monte Carlo techniques for the linearized model. The results obtained provide a complete analysis of congestion control algorithms for internet style networks with a single bottleneck node as well as for networks with general random topologies.     

一类互联电力系统的鲁棒联结稳定性分析

研究一类互联电力系统在不确定结构扰动下的鲁棒联结稳定问题．基于系统中互联矩阵的不确定性给出了鲁棒联结稳定的定义,利用向量Lyapunov函数方法及范数、特征值的性质推导了此类系统鲁棒联结稳定的两个充分条件．对系统在不确定结构扰动下联结稳定的鲁棒程度进行分析,得到了不确定参数的鲁棒界．两区域互联电力系统的仿真实例说明了所推导条件的有效性．     

不确定系统鲁棒LQ设计的稳定裕度分析和工程应用研究

针对不确定线性系统, 研究鲁棒LQ设计的稳定裕度分析问题. 首先提出不确定系统α_0裕度稳定鲁棒界, 针对结构和非结构不确定系统, 分别给出了鲁棒LQ控制系统的鲁棒稳定裕度性分析方法, 进一步给出对结构不确定系统优化鲁棒界的算法. 最后是造纸打浆过程实例的鲁棒稳定裕度性分析以及相应仿真结果.     

一阶系统预测PID控制器鲁棒稳定性分析

针对基于DCS预测PID的控制系统,利用Kharitonov定理和边缘理论分析其在参数不确定情况下输入/输出鲁棒稳定性。具体对一阶加纯滞后对象给出了系统保持稳定的最大过程参数区间。仿真结果表明,当过程参数偏离标称值时,该方法能使系统保持很好的鲁棒稳定性。     

Robust stability analysis of filtered Smith predictor for time-varying delay processes

This paper focuses on the robust stability analysis of the filtered Smith predictor (FSP) dead-time compensator for uncertain processes with time-varying delays. For this purpose, a delay-dependent LMI-based condition is used to compute a maximum delay interval and tolerance to model uncertainties such that the closed-loop system remains stable. Some simulation results illustrate that the proposed controller gives larger delays intervals or better performance than similar approaches proposed in literature applied both to stable and unstable processes.     

Robust stability analysis of discrete-time systems using geneticalgorithms

We reduce stability robustness analysis for linear, time-invariant, discrete-time systems to a search problem and attack the problem using genetic algorithms. We describe the problem framework and the modifications that needed to be made to the canonical genetic algorithm for successful application to robustness analysis. Our results show that genetic algorithms can successfully test a sufficient condition for instability in uncertain linear systems with nonlinear polynomial structures. Three illustrative examples demonstrate the new approach     

Robust stability analysis of constrained model predictive control

In this paper, we show that a constrained Model Predictive Controller, based on one plant model, stabilizes another plant if and only if some corresponding constrained Model Predictive Controller, based on the plant, stabilizes the plant. Thus strong nominal stability results can be used to analyze robust stability properties of some existing Model Predictive Control algorithms, without introducing any additional on-line computations and without modifying any of their attractive features. How the results may be used to synthesize robust controllers is also discussed. Examples are shown to illustrate the key ideas behind the approach.     

不确定系统的鲁棒稳定性

针对一类不确定非线性系统,基于王立新1994年提出的监督控制方案提出了一种SISO系统的模型参考自适应模糊控制器设计的新方案.该方案同时利用广义多线性模糊逻辑系统的逼近能力和I型模糊逻辑系统的逼近能力,不仅能保证闭环系统状态全局稳定,而且有效避免了控制增益可能出现的奇异性问题.理论分析证明了跟踪误差收敛到零,仿真结果表明了该方法的有效性.     

Robust stability analysis for uncertain delay systems with output feedback controller

A systematic approach is given in this paper for analyzing the robust stability of uncertain time-delay systems controlled by output feedback. By checking the eigenvalues of a Hamiltonian matrix, the stability of nominal systems can be examined first. Then, for the nominally stable uncertain systems with multiple time delays, a new method using structured singular value technique is proposed for finding a set of uncertain parameters within which the systems remain stable. Moreover, an illustrative example is given to show the usefulness of the proposed approach.     

Robust stability analysis and design method for the fuzzy feedbacklinearization regulator

A robust stability analysis and design method for a fuzzy feedback linearization regulator is presented. The well-known Takagi-Sugeno fuzzy model is used as the nonlinear plant model. Uncertainties and disturbance are assumed to be included in the model structure with known bounds. For these structured uncertainties, stability robustness of the closed system is analyzed in both input-output sense and Lyapunov sense. The robust stability conditions are proposed using multivariable circle criterion and the relationship between input-output stability and Lyapunov stability. Also, based on the stability analysis, a systematic design procedure for the fuzzy feedback linearization regulator is provided. The effectiveness of the proposed analysis and design method is illustrated by a simple example     

Robust stability analysis and stabilization for uncertain linear neutral delay systems

This paper considers the problem of robust stability analysis and robust stabilization for uncertain neutral delay systems. The system under consideration is subject to norm-bounded parameter uncertainty appearing in all the matrices of the state-space model. Both delay-dependent and -independent robust stability conditions are obtained in terms of linear matrix inequalities. Based on these, the corresponding conditions for the exsitence of robust stabilizing state feedback controllers are developed. When these conditions are feasible, the desired state feedback controller gain matrices can be obtained via convex optimization.     

NMPS基于DCS的预测PID控制器鲁棒稳定性分析

针对基于DCS的预测PID的控制系统,利用Kharitonov定理和边缘理论分析其在参数不确定情况下输入输出鲁棒稳定性。具体对NMPS（非最小相位系统）给出了系统保持稳定的最大过程参数区间。理论和分析仿真结果表明,当过程参数偏离标称值时,该算法能使系统保持很好的鲁棒稳定性。