r 阶鲁棒稳定性与零动态非渐稳单入单出系统的静态分叉控制镇定

研究零动态非渐稳的单输入单输出控制系统的局部渐近镇定问题,讨论了对这种系统镇定的设计方法,并对一类满足条件(S)的系统,利用静态分叉控制结果,提供了构造反馈控制函数使上述系统局部渐近镇定的方法.该方法也可看作是静态分叉控制在某些情况下的一种简化.     

分叉控制研究综述

回顾了近年来分叉控制的研究工作,展望了这一领域的研究方向,着重描述了分叉控制在非线性系统镇定问题中的原理和方法.􀁱     

具有状态和控制滞后的 线性时变时滞系统的输出反馈镇定

研究具有状态和控制滞后的线性时变时滞系统的静态输出反馈镇定，其设计过程只需解一个特殊的代数Ｒｉｃｃａｔｉ方程。并且指出，系统的动态输出反馈镇定问题可等价为广义系统的静态输出反馈镇定问题。最后通过实例论证了本方法的有效性。     

受控中心流形与非线性临界镇定

文中我们运用中心流形理论研究了临界非线性系统的局部渐近镇定问题,给出了可控临界指数的概念,在一定条件下得到了运用静态光滑反馈可镇定的充要条件。     

一般非线性控制系统的局部反馈渐近镇定

运用微分几何方法讨论了存在相对阶的一般非线性控制系统的局部反馈渐近镇定问题。在给出这类系统基于相对阶的标准形之后，如果其零动态渐近稳定，则可找到控制律局部镇定该系统。所得结果适用于一般非线性控制系统局部反馈渐近镇定的临界问题。     

不确定线性系统的输出反馈鲁棒H∞控制

研究了具有范数有界参数不确定线性系统的输出反馈鲁棒Ｈ∞控制问题，给出了该系统带Ｈ∞指标γ鲁棒稳定的充要条件，以及该系统静态输出反馈带Ｈ∞指标γ鲁棒镇定的充要条件，并且指出，系统的动态输出反馈鲁棒Ｈ∞镇定问题可等价为广义系统的静态输出反馈鲁棒Ｈ∞镇定问题，所给出的方法，其设计过程只需解一个特殊的Ｒｉｃｃａｔｉ方程最后通过实例论证了方法的有效性。     

一类单输入线性切换系统的可镇定性研究

考虑一类单输入线性切换系统的可镇定性问题,利用变结构控制对系统进行降维．通过对系统滑动模态的研究,得出了系统一致可镇定的充分条件和系统存在容许镇定策略的充分条件．给出了具体的容许镇定策略集合,并对二阶切换系统给出了详细的容许镇定策略．仿真实例验证了所提出结论的有效性．     

一类不确定非完整动力学系统的鲁棒镇定及其在移动机器人中的应用

本文讨论了一类带有未知惯性参数、动静态摩擦及外界干扰的非完整动力学系统的控制问题．基于变结构控制的思想，给出了该系统的镇定方法，使得Ｐｏｍｅｔ［３］关于非完整运动学系统的时变光滑镇定律可推广到相应的带有参数不确定和干扰的动力学系统上．最后，将所得结果应用于一类移动机器人的镇定控制，仿真结果验证了该方法的有效性．     

一类不确定非完整动力学系统的鲁棒镇定及其在移动机器人中的应用

本文讨论了一类带有未知惯性参数、动静态摩擦及外界干扰的非完整动力学系统的控制问题．基于变结构控制的思想，给出了该系统的镇定方法，使得Ｐｏｍｅｔ［３］关于非完整运动学系统的时变光滑镇定律可推广到相应的带有参数不确定和干扰的动力学系统上．最后，将所得结果应用于一类移动机器人的镇定控制，仿真结果验证了该方法的有效性．     

单参数离散时间非线性系统的可镇定性定理

本文对基本的离散时间非线性单参数随机系统建立了可镇定性定理. 该定理推进了文献[1]的结果, 进一步完 善了关于离散时间自适应控制的反馈能力刻画. 离散时间单参数系统可镇定的一个重要非线性临界常数是4, 用以刻画 关于幂函数类系统的反馈能力. 而作为本文定理的应用, 本文对一类典型的单参数离散时间非线性随机系统发现了新的 可镇定临界常数2.     

时滞反馈力作用下含有分数阶阻尼的随机系统的响应与分叉研究

分析了时滞反馈力作用下含有分数阶阻尼的随机系统,并讨论了该系统的稳态响应及随机分叉.首先,通过对含有时滞项的近似处理以及基于广义谐和函数的随机平均法得到了该系统的稳态响应.然后使用算例对方法的有效性进行了验证,其中主要研究了时滞反馈作用力和分数阶阻尼对系统稳态响应的影响,结果表明上述两者的变化会影响系统的稳态响应并引发随机分叉现象.     

Bifurcation stabilization of nonlinear systems by dynamic output feedback with application to rotating stall control

The paper deals with the problem of stabilization of stationary bifurcation solutions of nonlinear systems via dynamic output feedback.It is emphasized that the parameter of the system is not directly available.We introduce the concepts of uniform observability of the inverse of a function of state and input and N-order-input-to-state bifurcation stability.Based on the concepts,we propose a new method for designing dynamic compensators that guarantee bifurcation stability for the closed-loop system.As an example,we apply the general theory to active control of rotating stall in axial flow compressors by designing a stabilizing dynamic compensator for the three-state Moore-Greitzer model with a class of cubic compressor characteristics.     

Local feedback stabilization and bifurcation control, II. Stationary bifurcation

Local feedback stabilization and bifurcation control of nonlinear systems are studied for the case in which the critical linearized system possesses a simple zero eigenvalue. Sufficient conditions are obtained for local stabilizability of the equilibrium point at criticality and for local stabilizability of bifurcated equilibria. These conditions involve assumptions on the controllability of the critical mode for the linearized system. Explicit stabilizing feedback controls are constructed. The Projection Method of analysis of stationary bifurcations is employed. This work complements an earlier study by the same authors (Systems Control Lett.7 (1986) 11–17) of stabilization and bifurcation control in the (Hopf bifurcation) case of two pure imaginary eigenvalues of the linearized system at criticality.     

Bifurcations in the frequency response of nonlinear feedback control systems

The bifurcation theory is applied to bifurcations and accompanying jump phenomena which appear in the frequency response of nonlinear feedback control systems. It is also shown by a numerical example that such complicated structures exist in the frequency response of a simple nonlinear feedback control system.     

Feedback stabilization of bifurcations in multivariable nonlinear systems—Part II: Hopf bifurcations

In this paper we derive necessary and sufficient conditions of stabilizability for multi‐input nonlinear systems possessing a Hopf bifurcation with the critical mode being linearly uncontrollable, under the non‐degeneracy assumption that stability can be determined by the third order term in the normal form of the dynamics on the centre manifold. Stabilizability is defined as the existence of a sufficiently smooth state feedback such that the Hopf bifurcation of the closed‐loop system is supercritical, which is equivalent to local asymptotic stability of the system at the bifurcation point. We prove that under the non‐degeneracy conditions, stabilizability is equivalent to the existence of solutions to a third order algebraic inequality of the feedback gains. Explicit conditions for the existence of solutions to the algebraic inequality are derived, and the stabilizing feedback laws are constructed. Part of the sufficient conditions are equivalent to the rank conditions of an augmented matrix which is a generalization of the Popov–Belevitch–Hautus (PBH) rank test of controllability for linear time invariant (LTI) systems. We also apply our theory to feedback control of rotating stall in axial compression systems using bleed valve as actuators. Copyright © 2006 John Wiley & Sons, Ltd.     

一类具有饱和发生率的时滞恶意病毒传播模型的分岔控制策略

考虑非线性的饱和发生率,建立一种刻画信息物理融合系统(cyber-physical systems, CPS)中恶意病毒传播的SIRS(susceptible-infected-recovered-susceptible)模型.为了避免因Hopf分岔的产生致使恶意病毒传播扩散,采用参数调节法和状态反馈法相结合的混合分岔控制策略,研究信息物理融合系统的Hopf分岔控制问题,建立受控系统的稳定性条件和分岔判据,探明控制增益参数对Hopf分岔点和分岔极限环幅值的影响规律,并给出分岔阈值与增益参数间的关系图.数值仿真结果表明,所提出的混合分岔控制策略不仅能够改变Hopf分岔点的位置,而且可以有效调节极限环幅值的大小,使得信息物理融合系统产生预期的动力学行为,有效降低恶意病毒传播的危害.     

Algebraic condition of synchronization for multiple time-delayed chaotic Hopfield neural networks

In this paper, an easy and efficient method is brought forward to design the feedback control for the synchronization of two multiple time-delayed chaotic Hopfield neural networks, whose activation functions and delayed activation functions can have different forms of mapping. Without many complex restrictions and Lyapunov analytic process, the feedback control is given based on the M-matrix theory, the system parameters and the feedback section coefficients. All the results are simulated by Matlab and Simulink, which shows the simplicity and validity of the control. As shown in the simulation results, the error systems converge to zero rapidly.     

一类混沌系统的Hopf分岔控制

针对带参数的混沌系统,运用 Routh-Hurwitz判据及 Hopf分岔理论研究系统存在的动力学行为,设计状态反馈控制器对系统进行 Hopf分岔控制。分析系统参数及控制参数分别对系统稳定性与 Hopf分岔类型的影响,得到了系统稳定及不发生 Hopf分岔的系统参数条件。研究结果表明：控制器中的线性控制部分及非线性控制部分均能改变系统的分岔行为,使系统渐近稳定。数值仿真证明控制器设计的有效性。     

Further results on input-to-state stability for nonlinear systems with delayed feedbacks

We consider a class of nonlinear control systems for which stabilizing feedbacks and corresponding Lyapunov functions for the closed-loop systems are available. In the presence of feedback delays and actuator errors, we explicitly construct input-to-state stability (ISS) Lyapunov-Krasovskii functionals for the resulting feedback delayed dynamics, in terms of the available Lyapunov functions for the original undelayed dynamics, which establishes that the closed-loop systems are input-to-state stable (ISS) with respect to actuator errors. We illustrate our results using a generalized system from identification theory and other examples.     

一类脉冲动力系统的状态反馈控制

对一类具有状态反馈控制的脉冲动力系统的动力学性质进行了研究．由周期解的扰动解得到了一个Poincare映射，利用Poincare映射讨论了系统周期解的分岔，并得到了半平凡周期解和正周期-1解存在和稳定的充分条件．定性分析和数学模拟表明，半平凡周期解通过fold分岔分钻出正周期-1解，正周期-1解通过flip分岔分岔出正周期-2解，再通过一系列flip分岔通向混沌，此外，讨论了脉冲状态反馈控制的效果．