基于李雅普诺夫指数的离散混沌系统的控制研究

讨论了通过改变离散混沌系统的李雅普诺夫指数对离散混沌系统进行控制的一种方法。离散混沌系统的李雅普诺夫指数可按需要配置为负值，从而使系统收敛到任意的期望点上，仿真和实验结果表明，该控制方法是有效的，可以实现系统的快速稳定。     

无源性原理在鲁棒镇定中的应用

研究自由动态临界稳定仿射系统的输入到状态镇定,通过零状态可探测假设,减弱了通常的前提条件:自由动态全局渐近稳定;运用无源性原理研究扰动抑制,给出了输出负反馈解扰动抑制问题的简明条件.分析中用到Legendre-Fenchel变换.     

关于Sontag-Type控制的注记

基于控制李雅普诺夫函数的Sontag-Type控制是仿射系统鲁棒镇定中的重要控制律.首先揭示该控制律本质上是一种变结构控制且闭环的切换面总可达,受此启发并为了相对容易地构造控制李雅普诺夫函数,运用零状态可检测概念定义弱控制李雅普诺夫函数,并证明了基于弱控制李雅普诺夫函数的Sontag-Type控制的优化镇定性.文中还证明,在温和条件下,基于弱控制李雅普诺夫函数的Sontag＿Type控制为仿射系统的输入到状态镇定控制.     

基于李雅普诺夫稳定性的自适应模糊控制器设计

在动态系统模糊关系模型在线辨识的基础上,提出了一种用李雅普诺夫稳定性来进行自适应模糊控制器设计的新方法。仿真研究和实验装置应用均表明：该方法对于非线性、时滞过程的控制是有效的,具有实用价值。     

基于李雅普诺夫量子系统控制方法的状态调控

从多方面对基于李雅普诺夫的量子系统控制方法进行了系统深入地研究, 包括该方法与最优控制的关系; 李雅普诺夫函数与性能指标之间的关系; 几种常用李雅普诺夫函数下的控制所能解决的问题, 适用范围和所存在的问题等. 在此基础上, 结合量子系统本身所具有的特点, 分别针对本征态, 叠加态和混合态的制备与调控目标, 总结出多种不同控制问题的改进方案. 对不同改进方案的设计思想, 所能解决的问题, 物理意义及其适用范围等进行剖析, 系统化了一套基于李雅普诺夫稳定性理论对量子系统进行状态调控的设计方法.     

求解李雅普诺夫方程的U—D分解算法

本文提出了一种新的求解李雅普诺夫方程的数值解法——U-D分解法.其基本思想是将解矩阵P分解为单位上三角阵U和非负定对角阵D,因此将 P 的迭代求解化为其因子 U 和 D 的迭代.这样,在计算量基本不变的情况下,提高了解的精度.本文还对[1]中的加速收敛二步迭代法应用了 U-D 分解,使得该算法具有收敛快和精度高的双重优点.     

基于李雅普诺夫稳定性的模糊关系模型辨识算法*

本文在李雅普诺夫稳定性意义下，提出了一种辨识模糊关系模型的学习算法．仿真研究表明该算法简单易行，效果良好；可为模糊系统的辨识与控制提供了一条有效的途径．     

李雅普诺夫指数谱的研究与仿真

李雅普诺夫指数在研究动力系统的分岔、混沌运动特征中起着重要的作用。该文介绍了李雅普诺夫指数的定义、计算原理及数值计算的实现方法，应用Matlab软件，编制了计算李雅普诺夫指数的程序，分析了一维、二维和三维非线性动力系统中分岔和混沌与李雅普诺夫指数之间的关系。绘制了逻辑斯蒂映射、埃农映射和洛仑兹方程的分岔图，并计算了相应的李雅普诺夫指数。实例的计算机仿真表明李雅普诺夫指数是研究分岔、混沌运动，解决工程实际问题的有效方法之一。     

基于李雅普诺夫函数的BP神经网络算法的收敛性分析

针对前馈神经网络应时变输入的自学习机制，采用李雅普诺夫函数来分析权值的收敛性，从而揭示BP神经网络算法朝最小误差方向调整权值的内在因素，并在分析单参数BP算法收敛性基础上，提出单参数变调整法则的离散型BP神经网络算法．     

李雅普诺夫稳定性理论中V函数的构造研究

李雅普诺夫稳定性理论,在自动控制等方面有着很重要的作用,李雅普诺夫第二判别方法,可以直接判定微分方程组的稳定性,应用非常广泛,但是如何构造满足特定条件下的李雅诺夫函数V,则是微分方程组稳定性理论要解决的课题。本文通过实例分析总结,研究出了几种实用性强的李雅普诺夫函数V的构造形式和方法。     

A Survey on the Control Lyapunov Function and Control Barrier Function for Nonlinear-Affine Control Systems

This survey provides a brief overview on the control Lyapunov function(CLF) and control barrier function(CBF) for general nonlinear-affine control systems.The problem of control is formulated as an optimization problem where the optimal control policy is derived by solving a constrained quadratic programming(QP) problem.The CLF and CBF respectively characterize the stability objective and the safety objective for the nonlinear control systems.These objectives imply important properties including...     

On Assigning the Derivative of a Disturbance Attenuation Control Lyapunov Function

We consider feedback design for nonlinear, multi-input affine control systems with disturbances and present results on assigning, by choice of feedback, a desirable upper bound to a given control Lyapunov function (clf) candidate's derivative along closed-loop trajectories. Specific choices for the upper bound are motivated by ℒ₂ and ℒ_∞ disturbance attenuation problems. The main result leads to corollaries on “backstepping” locally Lipschitz disturbance attenuation control laws that are perhaps implicitly defined through a locally Lipschitz equation. The results emphasize that only rough information about the clf is needed to synthesize a suitable controller. A dynamic control strategy for linear systems with bounded controls is discussed in detail. Date received: March 27, 1998. Date revised: March 11, 1999.     

Stabilization of Nonlinear Systems with Filtered Lyapunov Functions and Feedback Passivation

In this paper a generalized class of filtered Lyapunov functions is introduced, which are Lyapunov functions with time‐varying parameters satisfying certain differential equations. Filtered Lyapunov functions have the same stability properties as Lyapunov functions. Tools are given for designing composite filtered Lyapunov functions for cascaded systems. These functions are used to design globally stabilizing dynamic feedback laws for block‐feedforward systems with stabilizable linear approximation.     

Construction of control Lyapunov functions for damping stabilization of control affine systems

This paper considers the stabilization of nonlinear control affine systems that satisfy Jurdjevic–Quinn conditions. We first obtain a differential one-form associated to the system by taking the interior product of a non vanishing two-form with respect to the drift vector field. We then construct a homotopy operator on a star-shaped region centered at a desired equilibrium point that decomposes the system into an exact part and an anti-exact one. Integrating the exact one-form, we obtain a locally-defined dissipative potential that is used to generate the damping feedback controller. Applying the same decomposition approach on the entire control affine system under damping feedback, we compute a control Lyapunov function for the closed-loop system. Under Jurdjevic–Quinn conditions, it is shown that the obtained damping feedback is locally stabilizing the system to the desired equilibrium point provided that it is the maximal invariant set for the controlled dynamics. The technique is also applied to construct damping feedback controllers for the stabilization of periodic orbits. Examples are presented to illustrate the proposed method.     

Multilayer Minimum Projection Method with Singular Point Assignment for Nonsmooth Control Lyapunov Function Design

Control Lyapunov function (CLF) design on a manifold is a difficult problem in control theory. To address this problem, we have proposed the multilayer minimum projection method. The method requires CLFs on different manifolds from the manifold where the control problem is defined. In this paper, we relax the requirement by desingularization of the functions on the manifolds. The paper focuses on the problem of desingularization in the multilayer minimum projection method. We show that the functions on other manifolds need not be CLFs by consideration of desingularization. Moreover, we propose a CLF design method by singular point assignment based on the advantage of desingularization. The method enables us to merge local CLFs into the global CLF. This paper proposes two CLF design methods: desingularization and singular point assignment. A CLF design example is provided for each method; the advantages of the proposed methods are confirmed by those two examples.     

Control Lyapunov functions for adaptive nonlinear stabilization

For the problem of stabilization of nonlinear systems linear in unknown constant parameters, we introduce the concept of an adaptive control Lyapunov function (aclf) and use Sontag's constructive proof of Artstein's theorem to design an adaptive controller. In this framework the problem of adaptive stabilization of a nonlinear system is reduced to the problem of nonadaptive stabilization of a modified system. To illustrate the construction of aclf's we give an adaptive backstepping lemma which recovers our earlier design.     

Homogeneous Feedback Control of Nonlinear Systems Based on Control Lyapunov Functions

This paper is concerned with homogeneous feedback control for a class of nonlinear systems. By using control Lyapunov functions, homogeneous controllers of homogeneous and nonhomogeneous systems are respectively constructed, under which the stabilization of the systems under considerations are guaranteed. Then, the design method is extended for uncertain systems by means of homogeneous domination theory. Compared with the traditional design method based on robust control Lyapunov functions, the present design reduces the difficulty of constructing controllers. Finally, several simulation examples are given to illustrate the correctness of the design.     

非线性定常系统及其定常Lyapunov函数的多项式等价类

非线性定常系统及其定常Ｌｙａｐｕｎｏｖ函数的多项式等价类苗原李春文杜继宏（清华大学自动化系北京１０００８４）关键词稳定性,非线性多项式系统,李亚普诺夫函数．收稿日期１９９５－０５－１６１引言李亚普诺夫第二方法作为处理系统稳定性问题的最主要的方法之一已...     

Lyapunov在电荷泵锁相环设计中的应用

状态空间方程描述的控制系统分析中广泛应用Lyapunov理论分析稳定性.因此,本文以具有一个零点的三阶电荷泵锁相环为例,建立了电荷泵锁相环的状态空间描述方程,并运用Lyapunov理论对其进行稳定性分析,且推导了其跟踪阶跃响应的能力.为了验证该方法的正确性,本文最后利用Verilog-AMS语言编写了电荷泵锁相环的行为级模型.模型仿真结果表明,控制系统的Lvapunov理论确实可以用来分析电荷泵锁相环的稳定性和阶跃响应.