一类线性切换系统基于带有时滞观测器的输出反馈镇定

许多切换系统的状态是不可测或不能完全可测的,从观测器设计的角度重新考虑了带有时滞的线性切换系统的输出反馈镇定问题.主要研究了观测器带有延时,且控制器也带有切换延时的情况,最终得到了系统可镇定的充分条件.     

广义分布参数系统的状态反馈稳定性问题(1)

关于系统的状态反馈稳定性问题的研究一直是现代控制理论研究的重要问题之一.广义分布参数系统是比分布参数系统更广的一类系统,在研究复合材料热导体中的温度分布等问题时会出现这样的系统.本文讨论了H ilbert空间中一阶广义分布参数系统的状态反馈稳定性问题.应用泛函分析及线性算子半群理论的方法给出了使闭环广义分布参数系统渐进稳定的充要条件,充分条件及状态反馈的构造性表达式.这对研究广义分布参数系统的状态反馈稳定性问题具有重要的理论价值.     

分数阶微分中立型系统的有限时间镇定性及有界性

讨论了一类分数阶微分中立型系统的有限时间状态反馈镇定性及有界性问题.利用Gronwall 不等式, 获得了使得系统有限时间状态反馈镇定及有限时间有界的充分性条件.     

Optimal NPID Stabilization of Linear Systems

We consider the problem of finding the optimal, robust stabilization of linear systems within a family of nonlinear feedback laws. Investigation of the efficiency of full-state based and partial-state based so-called NPID feedback schemes proposed for the stabilization of systems in robotic applications has provided the motivation for our work. We prove that, for a given quadratic Lyapunov function and a given family of nonlinear feedback laws, there exist optimal piecewise linear feedbacks that make the generalized Lyapunov derivative of the closed-loop system minimal. The result provides improved stabilization over the nonlinear stabilizing feedback law proposed in Ref. 1 as demonstrated in simulations of the Sarcos Dextrous Manipulator.     

一类线性系统的有限时间量化反馈控制问题

研究了一类带有不确定参数和外部扰动的线性系统的有限时间量化反馈控制问题.应用Lyapunov函数理论,通过量化反馈,使得系统鲁棒有限时间稳定.     

SISO多维控制系统的反馈镇定性及算法的数学机械化实现

从代数学的理想论以及代数簇理论,探讨了SISO多维控制系统的可反馈镇定条件,并给出反馈控制的表示.文中的主要结果建立在判定一个多变元多项式的零点集是否与由多项式刻画的凸集相交的前提之上,并用数学机械化方法实现了这一判定的过程.     

正则型控制系统的全局反馈镇定

在对非线性控制系统全局镇定的研究中 ,Byrness,Isidori讨论了光滑非线性系统的光滑反馈与全局正则型的等价条件 ;Kokotovic,Sussmann则在讨论了全局镇定的正实条件后 ,得到了一个判定系统为全局光滑可镇定的重要条件 .本文则考察一类正则型控制系统 ,通过变换系统和构造全局反馈镇定律的方法 ,得到全局光滑镇定     

基于输出反馈的一类大型互联非线性系统的鲁棒全局指数稳定

研究基于输出反馈的一类新的大型互联非线性不确定系统的鲁棒全局指数稳定问题,通过构造每个子系统收敛的状态观测器,并对观测器的状态作线性变换,得到鲁棒分散输出反馈控制器.当该反馈控制律作用于该系统时,闭环系统是全局指数稳定的.     

Numerical simulations for the stabilization and estimation problem of a semilinear partial differential equation

We deal with the numerical approximation of the problem of local stabilization of Burgers equation. We consider the case when only partial boundary measurements are available. An estimator is coupled with a feedback law in order to stabilize the discretized system. Two different feedback laws are compared. Their performance is analyzed in different domains related to idealized cardiovascular geometries, with increasing complexity.     

Algebraic Multiplicities Arising from Static Feedback Control Systems of Parabolic Type

In stabilization studies of linear parabolic control systems, a successful approach is a scheme employing dynamic compensators in the feedback loop. An essential reason is the fact that both sensors and actuators cannot be designed freely, especially in the case of boundary observation/boundary feedback. Most fundamental in this scheme is a simple stabilization result under the static feedback control scheme. In this scheme, little attention has been paid to how to assign new eigenvalues of the feedback system. In this article, we show a new feature of pole assignment that shows some choices of new eigenvalues cause a deterioration of the stability property. An algebraic growth rate is added to the feedback system in such a choice.     

基于输出反馈的一类大型互联Holder非线性系统的全局实际镇定

本文研究基于输出反馈的一类大型互联Holder连续非线性系统的全局实际镇定问题.通过构造每个子系统的状态观测器,并对观测器的状态作线性变换,得到分散输出反馈控制器.当输出反馈控制律作用于该系统时,闭环系统是全局实际稳定的.     

Stability analysis of linear parabolic systems and removement of singularities in substructure: Static feedback

We analyze stability property of a class of linear parabolic systems via static feedback. Stabilization via static feedback scheme is most difficult and challenging when both actuators and observation weights admit spillovers. This arises typically in the boundary observation-boundary feedback scheme. We propose a simple static feedback law containing a parameter γ, and enhance the stability property or achieve (slightly) stabilization. In some situations, the evolution of the substructure of finite dimension contains singularities regarding γ. We show that these singularities are removed as long as the dimension is not large.     

多时滞非线性中立型反馈系统的鲁棒稳定性

The stabilization of a class of neutral systems with multiple time-delays is considered. To stabilize the neutral system with nonlinear uncertainty, a state feedback control law via compound memory and memoryless feedback is derived. by constructed Lyapunov functional, delay-independent stability criteria are proposed that are sufficient to ensure a uniform asymptotic stability property. Finally, two concise examples are provided to illustrate the feasibility of our results.     

Asymptotic stability of nonlinear systems with unbounded delays

Some asymptotic stability criteria are derived for systems of nonlinear functional differential equations with unbounded delays. The criteria are described as matrix equations or matrix inequalities, which are computationally flexible and efficient. The theories are then applied to the stabilization of time-delay systems via standard feedback control (SFC) or time-delayed feedback control (DFC). Several examples are given to illustrate the results.     

Exponential stabilization of a class of nonlinear systems: A generalized Gronwall–Bellman lemma approach

In this paper, stabilizing control design for a class of nonlinear affine systems is presented by using a new generalized Gronwall–Bellman lemma approach. The nonlinear systems under consideration can be non Lipschitz. Two cases are treated for the exponential stabilization: the static state feedback and the static output feedback. The robustness of the proposed control laws with regards to parameter uncertainties is also studied. A numerical example is given to show the effectiveness of the proposed method.     

具有分布反馈和边界反馈的非均质Timoshenko梁的指数镇定性

讨论具有分布反馈控制和边界反馈控制的非均质Timoshenko梁的指数镇定问题.首先利用已有的关于线性分布参数系统的渐进稳定性判据,证明所论梁系统的能量可仅由一个分布反馈控制指数镇定.进而利用频域分片乘子方法,在所论梁系统同时具有分布反馈控制和边界反馈控制的条件下,证明其相应的闭环系统能量指数稳定.     

具有两个加性输入时滞系统的状态反馈控制

主要考虑了具有两个加性输入时滞的网络化控制系统的状态反馈控制问题.首先考虑具有两个加性时滞的系统稳定性,构造适当的Lyapunov泛函,不需要所有的矩阵正定,只需其整体正定.其次在估计Lyapunov泛函沿系统的导数时,针对时滞范围的不同,引入了不同的松弛矩阵,得出系统保守性较小的稳定条件.在此基础上,研究了系统状态反馈控制,最后得出闭环系统渐近稳定的充分条件,并给出控制器的设计方法.     

具有非线性扰动的不确定随机时变时滞系统的鲁棒镇定

本文研究了具有非线性扰动的不确定随机时变时滞系统的鲁棒镇定的问题.构造了适当的Lyapunov-Krasovskii泛函并利用自由权矩阵方法,借助于线性矩阵不等式(LMI)技术,设计了一个无记忆状态反馈控制器,并获得了不确定随机时变时滞系统的时滞依赖鲁棒镇定判据.数值例子及其仿真曲线表明所提出的理论结果是有效的.     

Structural constrained controllers for discrete-time linear systems

In this paper, we present an approach for designing structural constrained controllers for discrete-time linear systems, based on a new stabilizability property of the Riccati equation solution. First, the feedback stabilization problem under a general structural constraint is considered and a simple numerical procedure to solve it is presented. Special attention is given to the output feedback stabilization problem, for which sufficient conditions for the existence and convergence toward a stabilizing matrix are provided. Some examples are solved and comparisons with other methods available in the literature are made.This research has been developed with the financial support of the Conselho Nacional de Desenvolvimento Científico e Tecnológico, CNPq, Brasília, Brazil.     

Optimal feedback control of bilinear systems

Feedback synthesis of optimal constrained controls for single-input bilinear systems is considered. Quadratic cost functionals (with and without quadratic control penalization) are modified by the inclusion of additional nonnegative state penalizing functions in the respective cost integrands. The latter functions are chosen so as to regularize the problems, in the sense that feedback solutions of particularly simple form are obtained. Finite and infinite time horizon problem formulations are treated, and associated aspects of feedback stabilization of bilinear systems are discussed.