受多随机噪声和多随机脉冲干扰的非线性系统稳定性分析

针对一类受多有色噪声和多随机脉冲干扰的非线性系统(其中系统连续动态中的多随机噪声包含乘性和加性有色噪声且离散动态中多随机脉冲幅值的类型由一个齐次不可约非周期Markov链决定),分别提出概率意义和矩意义下的噪声-状态稳定性、概率意义下的全局渐近稳定性、矩意义下的指数稳定性判据.在脉冲数量受模态依赖平均脉冲区间约束下,首先基于乘性随机噪声的估计和Lyapunov函数方法,分别研究系统在矩意义下的噪声到状态稳定性和指数稳定性判据;然后基于乘性随机噪声满足大数定律的假设和Lyapunov函数方法,分别给出系统在概率意义下的噪声-状态稳定和全局渐近稳定的充分条件;最后通过仿真结果验证所提出稳定性判别准则的有效性.     

谐和与高斯白噪声联合作用下二自由度系统的随机稳定性研究

主要研究了谐和与高斯白噪声共同作用下二自由度系统的随机稳定性问题.首先,通过扩维的方式将非自治系统转化为自治系统.其次,利用摄动法和双傅里叶级数展开的方法求得了系统的矩Lyapunov指数与最大Lyapunov指数的近似解析结果,并和利用Monte Carlo仿真得到的数值结果进行了比较验证.最后,通过对系统矩Lyapunov指数和最大Lyapunov指数解析结果的研究分析,分别讨论了次谐共振和组合共振对系统随机稳定性的影响.     

随机Marino-Tomei系统的输出反馈鲁棒自适应跟踪

研究了一类Marino-Tomei非线性模型在不确定噪声干扰下的输出反馈鲁棒自适应跟 踪问题.通过滤波变换,采用随机控制Lyapunov设计方法,对于受方差未知的Wiener噪声干 扰的Marino-Tomei非线性系统,给出了参数自适应律和控制律,使得闭环系统成为噪声--状 态稳定的,并且跟踪误差的4次均方值在时间平均意义下收敛到一个足够小的区域内.     

类Lyapunov非线性系统降维观测器设计

对一般形式的非线性系统,引入了Lyapunov稳定意义下观测器存在性的概念,讨论了降维观测器的存在性.指出若相对于一特别形式的Lyapunov函数在Lyapunov稳定意义下存在全维观测器,则还存在降维观测器,并给出了降维观测器之设计方法.为说明该方法的指导意义,用该方法相对于Lipschitz非线性系统给出了降维观测器设计,并对该设计相对于一具体模型进行了仿真分析,仿真结果表明了该设计方法的正确性及实用性.     

具有均匀量化器的非线性网络控制系统的一致有界性

建立一种非线性连续被控对象、系统总时延小于一个采样周期的网络控制系统连续模型.通过线性化及离散化的方法将非线性系统转换一种离散化的模型.利用Lyapunov稳定性理论和线性矩阵不等式方法,设计控制方法使系统稳定.在系统包含均匀量化器的情况下,设计控制方法使系统一致有界.通过调节量化器的误差范围,可以将系统状态控制在一定的范围内.实际中,据此可设计相应的量化级别及编码长度等参数.通过仿真验证控制方法的有效性,并分析了量化误差对系统收敛性的影响.     

非线性不确定中立型系统的鲁棒H∞控制

考虑系统外界干扰、系统参数摄动等非线性扰动环节对中立型时滞系统的H∞影响,提出基于Lyapunov稳定性理论的鲁棒H∞控制器的设计思想.利用线性矩阵不等式(LMI)方法,给出了该类具有状态非线性不确定性中立型时滞系统的鲁棒∞控制器的设计实例.在非线性不确定函数满足增益有界的条件下,得到了该类时滞系统满足鲁棒∞性能的一个充分条件.通过求解一个线性矩阵不等式LMI,即可获得鲁棒∞控制器.仿真结果表明了基于Lyapunov稳定性理论,LMI技术设计的控制器克服了系统外界非线性干扰或系统本身非线性参数摄动的影响,实现了闭环系统的H∞性能条件下的渐近稳定,满足了该系统鲁棒H∞控制的要求.     

轧机自动位置控制系统混沌特性研究

针对轧机自动位置控制系统(APC)控制后的钢板不能准确停车,出现类似振动的现象,在考虑轧辊与钢板间的阻尼力、弹性力和轧辊偏心力的基础上,建立了一个轧机自动位置控制系统停车后的非线性模型.阐述了Lyapunov特性指数的计算方法,将Lyapunov指数作为APC系统非线性运动的混沌的判据.给出了Lyapunov指数与AP...     

具有状态时滞的切换随机系统的指数稳定条件

考虑由具有状态时滞的线性It(o)随机子系统构成的切换系统,基于多Lyapunov泛函方法研究切换与时滞对于稳定性的共同影响,并以此建立均方指数稳定条件.在均方意义下噪声对于稳定性的影响基本是负面的,因此构造一类形式较为一般的Lyapunov泛函并运用噪声的统计特性于其解析过程中,以减少噪声所引起的保守性.最后,通过一个仿真算例描述切换与时滞的相互制约关系表明了所提出方法的有效性.     

芾有干扰的非线性系统的无源化控制

本文提出并考察一类带有干扰的非线性系统的无源化控制问题,即构造反馈控制器使得相应的闭环系统无源且保持内部稳定.本文给出了在此馈通项下系统无源的一个充分必要条件.另外,针对两类特殊情形下的无源控制,应用Lyapunov递归方法得到了解决该问题的一个条件;特别利用控制Lyapunov函数,对较一般情形的非线性系统构造出一类有效的无源化控制器.     

多变量时间序列最大Lyapunov指数的噪声估计

在Rosenstein等人研究工作的基础上,提出了一种计算多变量混沌时间序列最大Lyapunov指数的改进的小数据量算法。以Ikeda映射、Henon映射、Lorenz映射和Chen映射四种典型混沌系统为例,采用将随机数方法生成的高斯白噪声与多变量混沌时间序列叠加的方法,分析了相同信噪比下,数据量对最大Lyapunov指数的影响;以及不同信噪比下,混沌时序最大Lyapunov指数的变化趋势。研究结果表明：当加入一定范围信噪比的噪声时,多变量时间序列的最大Lyapunov指数受到的扰动影响很小。     

Stability in Probability and Inverse Optimal Control of Evolution Systems Driven by Lévy Processes

This paper first develops a Lyapunov-type theorem to study global well-posedness(existence and uniqueness of the strong variational solution)and asymptotic stability in probability of nonlinear stochastic evolution systems(SESs)driven by a special class of Levy processes,which consist of Wiener and compensated Poisson processes.This theorem is then utilized to develop an approach to solve an inverse optimal stabilization problem for SESs driven by Levy processes.The inverse optimal control design achieves global well-posedness and global asymptotic stability of the closed-loop system,and minimizes a meaningful cost functional that penalizes both states and control.The approach does not require to solve a Hamilton-Jacobi-Bellman equation(HJBE).An optimal stabilization of the evolution of the frequency of a certain genetic character from the population is included to illustrate the theoretical developments.     

基于平方和的一类不确定非线性系统的鲁棒稳定性

针对模型参数不确定的一类非线性系统,用基于平方和的方法设计了非线性状态反馈控制器。基于平方和的方法可以利用半正定问题将搜索李亚谱诺夫方程及非线性控制器结合在一起,该方法比一般近似线性化或者反馈线性化保守性更低。仿真结果表明了所设计控制器的有效性和可行性。     

Stability analysis of planar systems with nilpotent (non-zero) linear part

A simple necessary and sufficient condition for asymptotic stability of the origin is derived for a large class of planar nonlinear systems that cannot be studied by means of their linearization, which is nilpotent and not zero. The condition is based on the use of Darboux polynomials, to derive a Lyapunov function for the first approximation of the system with respect to a vector function representing a dilation. Results by Andreev (1958), on the qualitative behaviour of equilibrium points, and the Belitskii normal form are used in the proofs. The proposed condition is applied to the asymptotic stabilization of the origin, for a class of planar systems whose linearization cannot be stabilized.     

一类具有L∞范数有界扰动的非线性系统鲁棒控制

首先针对不确定非线性系统,基于L∞范数定义了鲁棒稳定化和鲁棒跟踪控制问题.然后利用反馈线性化技术和Lvapunov方法,设计了相应的鲁棒控制器.仿真结果验证了控制器设计的正确性.     

面向光伏MPPT控制策略的改进果蝇算法

局部遮光会降低光伏发电系统的效率。在局部遮光条件下,光伏系统的输出功率特性曲线会产生多个峰值,传统的最大功率跟踪方法不具有全局搜索的能力,其在进行多峰值最大功率跟踪时会失效。果蝇算法(Fruit Fly Optimization Algorithm,FOA)具有全局寻优能力,但是在求解过程中存在收敛速度慢、收敛精度低及容易收敛于局部最优值的问题。文中对果蝇算法进行改进,提出结合自适应lévy飞行步长的Lévy-FOA算法,该算法充分利用Lévy飞行不均匀随机游走的特性,引入自适应步长调整因子,改进了原有算法的位置更新方式,提高了算法的收敛速度以及收敛精度,避免了算法陷入局部极值。文中利用3个标准函数对自适应Lévy-FOA算法的收敛性进行分析,并与普通FOA算法、自适应改进学习因子粒子群算法(Adaptive Particle Swarm Optimization,APSO)进行对比。结果表明,与FOA算法和APSO算法相比,自适应Lévy-FOA算法的平均跟踪时间有较大幅度的减少,平均收敛精度提高了4个数量级。最后,将自适应Lévy-FOA算法应用于光伏最大功率跟踪中。仿真结果显示,在不同的光照条件下,自适应Lévy-FOA算法能够经过较少的迭代实现最大功率跟踪,并且在第一次迭代后就能达到最大功率的90%以上,与其他算法的跟踪效果对比,自适应Lévy-FOA算法具有较短的跟踪时间和较高的跟踪精度,实际寻优能力优越,能够提高光伏系统的输出效率。     

On stability analysis via Lyapunov exponents calculated based on radial basis function networks

The concept of Lyapunov exponents is a powerful tool for analysing the stability of nonlinear dynamic systems, especially when the mathematical models of the systems are available. For real world systems, such models are often unknown. Estimating Lyapunov exponents using a time series has the advantage in that no mathematical model is required. However the time-series-based methods are believed to be reliable only for estimating positive exponents. Furthermore, when nonlinear mapping is applied for deriving the neighbourhood-to-neighbourhood matrices, the loads of mathematical deduction and programming increase significantly, which makes it unfeasible to nonlinear systems with high dimensions. In contrary, the model-based methods are constructive and reliable for calculating both positive and non-positive exponents. The use of the system Jacobians is the key to the advantage of the model-based methods. In this article, a novel approach is proposed, where the system Jacobians are derived based on system approximation using the radial basis function network. The proposed method inherits the advantage of the model-based methods, yet no mathematical model is required. Two case studies are presented to demonstrate the efficacy of the proposed method. We believe that the work can contribute to the stability analysis of nonlinear systems of which the dynamics are either difficult to model due to complexities or unknown.     

A Global Maximum Error Controller Based Nonlinearity Aware TPWL Method for Reducing Nonlinear Systems

Abstract

Model order reduction is a common practice to reduce large order systems so that their simulation and control become easy. Nonlinearity aware trajectory piecewise linear is a variation of trajectory piecewise linearization technique of order reduction that is used to reduce nonlinear systems. With this scheme, the reduced approximation of the system is generated by weighted sum of the linearized and reduced sub-models obtained at certain linearization points on the system trajectory. This scheme uses dynamically inspired weight assignment that makes the approximation nonlinearity aware. Just as weight assignment, the process of linearization points selection is also important for generating faithful approximations. This article uses a global maximum error controller based linearization points selection scheme according to which a state is chosen as a linearization point if the error between a current reduced model and the full order nonlinear system reaches a maximum value. A combination that not only selects linearization points based on an error controller but also assigns dynamic inspired weights is shown in this article. The proposed scheme generates approximations with higher accuracies. This is demonstrated by applying the proposed method to some benchmark nonlinear circuits including RC ladder network and inverter chain circuit and comparing the results with the conventional schemes.     

移动机器人的全局轨迹跟踪控制

考察了移动机器人的轨迹跟踪问题,针对以前沿袭线性化的思路设计的控制律带来 的局部稳定特性,基于后退(backstepplng)方法的思想设计了具有全局渐近稳定的跟踪控制 器.该方法将系统分解为低阶子系统来处理,利用中间虚拟控制量和部分Lyapunov函数简 化了控制器的设计并具有直观的稳定性分析.仿真结果验证了所设计控制器的有效性.     

Successive linearizations of second order multidimensional time-invariant systems

The present paper discusses a linearization method for second order multidimensional time-invariant systems. The method approximates locally the nonlinear vector field around the equilibrium, where the solution starting from a given initial state near the equilibrium is approximated by a linear solution. This linearization is usually called local trajectory-based linearization. The approximation is computed using an iterative method, which consists of successive approximations in the least square sense. Using a numerical example, it is shown that the linearized solutions exhibit good agreement with the nonlinear solutions.     

非线性控制系统的近似化方法

介绍了目前几种较常用的非线性控制系统近似化方法包括伪线性方法、扩展线性方法、近似输入／输出线性化、近似反馈线性化、中心流形及平均法等,对有关的理论与应用研究进展作了较全面的综述。