基于Riccati 方程解的非线性降维观测器

对Lipschitz非线性系统降维观测器进行讨论，在代数Riccati方程有正定解的前提下，指出Lipschitz非线性系统存在降维观测器，它取决于所考虑的代数Riccati方程的正定解。给出了降维观测器的设计方法，机器人模型的仿真结果表明其具有实用性。     

二阶线性系统全维PI观测器的参数化设计

基于一类广义Sylvester矩阵方程的解．提出了二阶线性系统的全维PI观测器设计参数化方法．给出了该类观测器的增益矩阵和左特征向量矩阵的参数化表达式．该观测器设计的参数化方法直接基于二阶线性系统的参数矩阵，不涉及系统的变换或增广．数值例子表明了所提方法的简单有效性．     

一类关联时滞系统的分散稳定化控制器设计

应用Lyapunov稳定性理论,提出一类关联时滞系统能用分散线性状态反馈镇定的充分条件,进而证明了该条件等价于子系统级上N个带参数的代数Riccati矩阵方程的正定解的存在性,并利用这些正定解矩阵给出了相应的稳定化分散控制器。应用所提出的方法,可望得到具有更小反馈增益参数的分散稳定化控制律。     

二阶动力学系统高阶PI观测器的参数化设计方法

本文研究二阶动力学系统的高阶比例积分(PI)观测器设计问题．基于Sylvester矩阵方程的解，提出了该观测器设计的参数化方法．该参数化方法给出了该类观测器增益矩阵的参数化表达式，其所含参数除了满足两个约束条件之外是完全自由的．这些参数为控制系统设计提供了全部自由度，可通过优化等手段选择这些参数来满足某些性能要求，如干扰解耦、故障检测和鲁棒性等．此外，该PI观测器的参数化设计方法直接利用二阶动力学系统的原始参数矩阵，只涉及二阶动力学系统n维参数矩阵的运算．给出一个数值例子，以说明所提方法的简单性和有效性．     

逆系统方法中非线性系统状态观测器的应用

将Lipschitz非线性系统状态观测器设计方法应用于非线性系统的逆系统方法设计中,解决了在利用逆系统方法实现非线性系统反馈线性化的过程中由于系统状态的不可知,而使系统不能满足反馈补偿的问题。针对以往的Lipschitz非线性系统状态观测器设计方法中通过Riccati方程对增益矩阵的求取过程比较繁琐的问题,着重讨论了采用线性矩阵不等式来改进增益矩阵的求取方法,利用Matlab中的LMI工具箱对其进行求取,计算简单,并给出了证明。最后通过实例仿真,验证了方法的有效性。     

离散线性系统高阶积分观测器设计

针对离散线性系统提出一类高阶积分观测器。并且显示这类观测器满足极点配置分离原理，同时给出了这类观测器的存在条件．基于Sylvester矩阵方程的显式参数化通解提出了这类观测器的参数化设计方法．该方法不仅给出了观测器增益矩阵的参数表达式，而且还提供了观测器系统矩阵左特征向量的参数表达式．该设计方法给出了所有的设计自由度，为实现系统的其他性能提供了方便且强有力的工具．数值例子说明了设计过程，并表明了该方法的有效性．     

关于不确定的对称组合系统的稳定化控制器与观测器的设计

本文研究了不确定的对称组合系统的稳定化控制器与观测器的设计问题，给出一种设计稳定化控制器与观测器的方法，在这种设计方法中，使给定的带有不确定性的对称组合系统稳定的状态反馈增益矩阵和观测器增益矩阵可由低阶代数Ｒｉｃｃａｔｉ方程的解导出。     

时滞Lipschitz非线性系统观测器设计

给出了满足Lipschitz条件的离散非线性时滞系统的全维、降维观测器的设计方法和误差收敛的充分条件,并分别进行了证明.全维观测器通过将带有非线性项的矩阵不等式转化为两步线性矩阵不等式解出两个增益矩阵.降维观测器则通过解线性矩阵不等式(LMI)方便地获得观测器的增益矩阵,消除了增益矩阵选取的盲目性.通过对同一模型的仿真分析,两种观测器的状态估计误差均能迅速收敛到0,表明了所提出方法的有效性.     

非线性系统观测器的设计:LMI方法

对满足Lipschitz条件的非线性系统给出了全维、降维观测器存在的充分条件并分别进行了证明,重点设计了新形式的降维状态观测器,观测器增益矩阵的获得完全取决于线性矩阵不等式(LMI)的解的情况,应用线性矩阵不等式工具箱使得设计更加方便,消除了增益矩阵选取的盲目性.通过对实际模型的仿真分析可知,两种观测器的状态估计误差均能渐近收敛到零,表明了该方法的有效性.     

Lipschitz广义非线性系统观测器设计

研究一类广义非线性系统的观测器设计问题．首先讨论了半正定Lyapunov函数下指数1广义非线性系统稳定及渐近稳定性,然后对一类由线性和Lipschitz非线性项组成的广义非线性系统,给出了渐近稳定观测器存在的条件,并把观测器反馈增益矩阵的设计归结为广义线性系统容许控制以及奇异值计算问题,证明了若容许广义线性系统矩阵的最小奇异值大于系统的Lipschitz常数,容许控制器增益矩阵就是待求的观测器反馈增益矩阵。     

Control design based on a linear state function observer

A control design method based on a linear state function observer is proposed. The method is a semi-inverse design procedure in that the control law is not designed before the observer system, but is a result of the observer design. However, the observer design is not completely independent of the control design, but seeks to yield a feedback signal that is close to a prescribed control law. First, the observer design problem is considered as the reconstruction of a linear function of the state vector. The linear state function to be reconstructed is the given control law. Then, based on the derivation for linear state function observers, the observer design is formulated as a parameter optimization problem. The optimization objective is to generate a matrix that is close to the given feedback gain matrix. Based on that matrix, the form of the observer and a new control law can be determined. The semi-inverse design procedure can yield a reduced-order observer with dimension considerably smaller than that of the system. Two numerical examples are used to demonstrate the proposed design procedure.     

线性广义系统的区间观测器设计

本文研究了连续时间线性广义系统的区间观测器设计问题.首先根据正系统的稳定性判据提出了一种基于线性矩阵不等式的广义区间观测器直接设计法,然后通过引入更多的设计自由度进一步放宽了区间观测器的设计条件,扩大了设计方法的适用范围.所提出的设计方法无需坐标变换,是一种直接设计方法.最后,通过两个仿真算例验证了所提出方法的有效性.     

具有单调性非线性项的非线性系统降维观测器设计

Based on the discussion about the existence and design method of full-order observer for systems with monotone nonlinearities, a reduced-order observer design method is developed under the assumption that a linear matrix inequality (LMI) has positive definite matrix solution and the reduced-order observer gain matrix is computed by the solution of LMI. By a linear transformation, a reduced-order observer which does not contain the information of the derivative of the system output is provided. A model is simulated and some conclusions are drawn based on the comparison of the results of reduced-order observer to that of full-order observer. The simulation shows that the design method developed by this paper has good performance.     

Design of multifunctional reduced order observers†

This paper presents a method for the design of an observer capable of reconstucting several linear functionals of the states of a linear, finite-dimensional system. The goal of this method is the design of an observer having minimum order subject to the restriction that the observer eigenvalues be freely assignable. The method is based on the reduction of a state observer formulated from an observable canonic form for the system when the functionals are treated as if they were additional outputs.     

Nonlinear robust observer design using an invariant manifold approach

This paper presents a method to design a reduced order observer using an invariant manifold approach. The main advantages of this method are that it enables a systematic design approach, and (unlike most nonlinear observer design methods), it can be generalized over a larger class of nonlinear systems. The method uses specific mapping functions in a way that minimizes the error dynamics close to zero. Another important aspect is the robustness property which is due to the manifold attractivity: an important feature when an observer is used in a closed loop control system. A two degree-of-freedom system is used as an example. The observer design is validated using numerical simulation. Then experimental validation is carried out using hardware-in-the-loop testing. The proposed observer is then compared with a very well known nonlinear observer based on the off-line solution of the Riccati equation for systems with Lipschitz type nonlinearity. In all cases, the performance of the proposed observer is shown to be very high.     

非线性系统降维观测器设计

对Lipschitz非线性系统降维观测器进行了讨论.首先考虑了降维观测器存在之条件, 然后给出了此条件下的降维观测器的具体设计方法,该设计方法基于与非线性函数的Lipschitz 常数有关的代数Riccati不等式的求解.最后,针对一个具体实际控制模型的仿真,验证了文中 所提出之方法的实用性.     

Design of optimal interval observers using set‐theoretic methods for robust state estimation

This article aims to design an optimal interval observer for discrete linear time‐invariant systems. Particularly, the proposed design method first transforms the interval observer into a zonotopic set‐valued observer by establishing an explicit mathematical relationship between the interval observer and the zonoptopic set‐valued observer. Then, based on the established mathematical relationship, a locally optimal observer gain is designed for the interval observer via the equivalent zonotopic set‐valued observer structure and the Frobenious norm‐based size of zonotopes. Third, considering that the dynamics of the optimal interval observer becomes a discrete linear time‐varying system due to the designed time‐varying optimal gain, an optimization problem to obtain a coordinate transformation matrix and the locally optimal observer gain for the interval observer is formulated and handled. Finally, a theoretic comparison on the conservatism of the interval observer and the zonotopic set‐valued observer is made. At the end of this article, a microbial growth bioprocess is used to illustrate the effectiveness of the proposed method.     

基于区间观测器的动态系统故障诊断技术综述

介绍一种基于区间观测器的故障诊断技术.为突出区间观测器在故障诊断方面的优势,总结归纳针对不同类型系统构造的可以达到故障诊断目的的区间观测器,并讨论观测器的设计条件.例如,事件触发机制下的故障检测区间观测器,针对线性参数变化系统设计的基于区间观测器的故障检测机制,在区间观测器的框架下实现带有未知互联项的T-S模糊大系统的故障隔离,以及利用区间观测器对多智能体系统实现故障隔离.最后探讨该领域亟待解决的问题.     

基于观测器的一类连续非线性系统的采样控制

首先使用反演方法分别设计了系统的连续时间状态反馈控制器、连续时间观测器和基于连续时间观测器的连续时间控制器. 接下来, 利用零阶保持法对连续时间状态反馈控制器进行离散化, 获得了状态反馈采样控制器; 利用零阶保持法对基于连续时间观测器 的连续时间控制器离散化, 获得了基于连续时间观测器的采样控制器; 利用Euler法对连续时间观测器离散化, 同时利用零阶保持法对控制器离散化, 从而获得了采样观测器和基于采样观测器的采样控制器. 本文论证了上述状态反馈采样控制器和基于连续时间观测器的采样控制器可以保证闭环系统渐近稳定, 而基于采样观测器的采样控制器可以保证被控对象的状态是有界的, 其最终边界依赖于设计参数与采样周期. 最后, 通过选择适当的采样周期, 完成了闭环采样控制系统的设计. 一个船舶航向控制的例子表明应用本文 所提方法设计出的三种采样控制器具有良好的控制效果.