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.     

仿射非线性系统的一种观测器设计方法

对仿射非线性系统全维观测器设计方法进行了讨论，提出了一种设计方法．该方法基于微分Riccati方程的正定解，观测器的增益矩阵通过Riccati方程的正定解给出，因而观测器增益矩阵为时变的．通过坐标变换，用李亚普诺夫方法对观测器的存在性进行了论证．对一个实际模型的仿真分析表明了该方法的实用性和正确性．     

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.     

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.     

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.     

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。     

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。     

一类非线性组合大系统的稳定性

本文研究一类比较广泛的非线性组合大系统的稳定性问题.基于矩阵代数Riccati 方程存在对称正定解的新判据(引理2),给出了检验这类非线性组合大系统稳定性的新准 则,所给出的稳定性准则只涉及子系统的稳定性以及子系统之间的互联项,因此,当应用该准 则检验这类非线性组合大系统的稳定性时,避免了构造子系统以及大系统的Lyapunov函数 的困难.     

非线性系统指数型降维观测器设计

1 引言 控制系统的状态反馈对各种综合问题显示了其极大的优越性,但系统状态通常不可直接测量到,这就有必要引入状态观测器.对线性系统,著名的Kalman滤波器和Luenberger观测器设计方法为其提供了较为完善的答案.对非线性系统而言,观测器设计是一项具有复杂性的研究工作并引起了众多人的关注.通常来说,有这样几类非线性观测器设计方法:扩展Kalman 滤波器[1]及扩展Luenberger观测器方法[2],非线性坐标变换法[3～5]及类Lyapunov方法[6～10].与线性系统一样,非线性系统按其结构可分为全维观测器和降维观测器.本文对Lipschitz非线性系统降维观测器设计方法进行了讨论.     

求解对偶Riccati方程的矩阵符号函数法

本文介绍一种求解对偶代数Riccati方程正定(负定)稳定(反稳定)解的方法——矩阵符号函数法,给出这些解的唯一存在的充分必要条件和算法实现。     

非线性MIMO系统的降维状态观测器

研究一类多输入多输出（ＭＩＭＯ）非线性时变系统的降维状态观测器设计问题,提出了一种非线性降维状态观测器设计方案,并从理论上证明了状态观测误差的指数收敛性,其中设计的降维状态观测器具有收敛速度可调的特性,最后给出了数值算例,仿真结果表明了本文方法的有效性。     

Study on Four Disturbance Observers for FO-LTI Systems

This paper addresses the problem of designing disturbance observer for fractional order linear time invariant (FO-LTI) systems, where the disturbance includes time series expansion disturbance and sinusoidal disturbance. On one hand, the reduced order extended state observer (ROESO) and reduced order cascade extended state observer (ROCESO) are proposed for the case that the system state can be measured directly. On the other hand, the extended state observer (ESO) and the cascade extended state observer (CESO) are presented for another case when the system state cannot be measured directly. It is shown that combination of ROCESO and CESO can achieve a highly effective observation result. In addition, the way how to tune observer parameters to ensure the stability of the observers and reduce the observation error is presented in this paper. Finally, numerical simulations are given to illustrate the effectiveness of the proposed methods.      

Full‐Order and Reduced‐order Observer Design for a Class of Fractional‐order Nonlinear Systems

The paper is concerned with problem of the full‐order and reduced‐order observer design for a class of fractional‐order one‐sided Lipschitz nonlinear systems. By introducing a continuous frequency distributed equivalent model and using indirect Lyapunov approach, the sufficient condition for asymptotic stability of the full‐order observer error dynamic system is presented. Furthermore, the proposed design method was extended to reduced‐order observer design for fractional‐order nonlinear systems. All the stability conditions are obtained in terms of LMI, which are less conservative than some existing ones. Finally, a numerical example demonstrates the validity of this approach.     

Hybrid dead-beat observers for a class of nonlinear systems

This paper studies both the full order and the reduced order dead-beat observer problem for a class of nonlinear systems, linear in the unmeasured states. A novel hybrid observer design strategy is proposed, with the help of the notion of strong observability in finite time. The proposed methodology is applied for the estimation of the frequency of a sinusoidal signal. The results show that accurate estimation can be provided even if the signal is corrupted by high frequency noise. A brief discussion of the robustness properties of the proposed observer with respect to measurement errors is also provided.     

Disturbance localization and pole shifting by dynamic compensation

This paper concerns the problem of disturbance localization and pole shifting by dynamic compensation in multivariable linear systems with inaccessible state vector. A necessary and sufficient condition for the solvability of the problem is given. Two synthesis procedures of the compensator are presented: one is based on an observer and the other is based on a dual observer. The observer designed by the proposed procedure acts as as unknown input observer for a linear function. An improved procedure of designing a reduced order unknown input observer is also given. The result may be applicable to reducing the compensator order.     

Wavelet reduced order observer based adaptive tracking control for a class of uncertain nonlinear systems using reinforcement learning

This Paper investigates the mean to design the reduced order observer and observer based controllers for a class of uncertain nonlinear system using reinforcement learning. A new design approach of wavelet based adaptive reduced order observer is proposed. The proposed wavelet adaptive reduced order observer performs the task of identification of unknown system dynamics in addition to the reconstruction of states of the system. Reinforcement learning is used via two wavelet neural networks (WNN), critic WNN and action WNN, which are combined to form an adaptive WNN controller. The “strategic” utility function is approximated by the critic WNN and is minimized by the action WNN. Owing to their superior learning capabilities, wavelet networks are employed in this work for the purpose of identification of unknown system dynamics. Using the feedback control, based on reconstructed states, the behavior of closed loop system is investigated. By Lyapunov approach, the uniformly ultimate boundedness of the closed-loop tracking error is verified. A numerical example is provided to verify the effectiveness of theoretical development.     

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.     

Analysis and control of the jump modes behavior of 2-D singular systems—Part II: Regular observer and compensator design

This paper considers the problems of regular observer and compensator design for 2-D acceptable singular systems. First, the notions of jump mode reconstructability and jump mode reachability for 2-D acceptable singular systems are proposed. Necessary and sufficient conditions are presented for the jump mode reconstructability and reachability, respectively. Then, we show that there exists a reduced order regular observer for a 2-D acceptable singular system if the system is detectable and jump mode reconstructable, while there exists a reduced order regular compensator for a 2-D acceptable singular system if the system is stabilizable and jump mode reachable.     

Dynamic output feedback sliding mode control for nonminimum phase linear systems with disturbance attenuation

A sliding mode control algorithm using output information only is developed in this paper for a linear system with mismatched disturbance. The nominal system is allowed to be nonminimum phase. A scheme designed to combine the output‐dependent integral sliding surface with a reduced‐order observer is proposed. Utilizing an H_∞ control analytical technique, once the system is in the sliding mode, the proposed algorithm can guarantee robust stabilization and sustain the nature of performing disturbance attenuation when the solution to one algebraic Riccati inequality can be found. A controller is designed to satisfy the reaching and sliding condition in line with the reduced‐order observer. Finally, a numerical example is explained to show the applicability of the proposed scheme. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society