一类不确定性拟单边Lipschitz非线性系统观测器设计

本文研究了一类不确定性拟单边Lipschitz非线性系统观测器设计问题.利用拟单边Lipschitz条件代替通常的Lipschitz条件,得到了这类不确定性非线性系统观测器设计的线性矩阵小等式判据.结果推广了该类系统鲁棒H∞观测器问题.文末,给出了几个仿真算例以验证所给方法的正确性.     

基于观测器的非严格反馈时滞非线性系统的神经网络自适应控制

针对一类非严格反馈的时滞非线性系统, 研究了一类基于观测器的自适应神经网络控制问题.针对系统中存在未知状态变量的问题, 设计了一个状态观测器.利用反步法和径向基神经网络的逼近特性, 提出了一种自适应神经网络输出反馈控制方法.所设计的控制器保证了闭环系统中所有信号的半全局一致有界性.最后, 通过仿真验证了所提控制方法的有效性.     

一类时滞Lipschitz非线性离散广义系统观测器的设计

针对一类时滞Lipschitz非线性离散广义系统,主要研究了系统的观测器设计问题.首先,基于广义系统的特殊结构对时滞广义系统进行变换,将系统转化为易于求取观测器的形式;其次,考虑到系统中的Lipschitz非线性项,将系统分两种情况并分别设计出了系统的观测器;最后,为保证系统与观测器的误差系统渐近稳定,通过利用线性矩阵不等式(LMI)的方法给出了两个观测器存在的条件,并通过数值例子验证了观测器设计方法的有效性.     

一类离散时间非线性系统降维观测器设计

本文研究了一类离散时间非线性系统降维观测器设计问题.利用微分中值定理和Schur补,得到了这类非线性系统降维观测器的设计判据.所给判据为线性矩阵不等式形式.与现在已有文献中的判据相比,本文得到的判据不仅可用于离散时间可微Lipschitz非线性系统而且可用于某些离散时间的非Lipschitz非线性系统.文末,给出了几个仿真算例以验证所得结论的正确性.     

基于模糊与神经网络技术的复杂非线性跟踪控制

针对一类具有不确定性、多重时延和状态未知的复杂非线性系统,把模糊T-S模型和RBF神经网络结合起来,提出了一种基于观测器的跟踪控制方案.首先,应用模糊T-S模型对非线性系统建模,设计观测器用来观测系统状态,并由线性矩阵不等式得到模糊模型的控制律;其次,构建了自适应RBF神经网络,应用自适应RBF神经网络作为补偿器来补偿建模误差和不确定非线性部分.证明了闭环系统满足期望的跟踪性能.示例仿真结果表明了该方案的有效性.     

一类随机非线性马尔可夫切换系统的输出反馈控制

研究了一类具有马尔可夫切换的随机非线性系统的输出反馈镇定问题.利用非线性增益观测器设计方法,结合反推技术,设计了输出反馈控制器,保证了闭环系统几乎处处有唯一解且闭环系统是几乎处处渐近稳定的.数值仿真验证了输出反馈控制器的有效性.     

增长依赖于不可测状态非线性系统量化输出反馈控制设计

研究了一类不确定非线性系统的量化输出反馈控制设计问题.不同于现有文献,所研究系统的非线性增长依赖于不可测状态.这使得现有文献中的观测器设计方法不再适用,且闭环系统性能分析更为复杂和困难.文章首先引入了一个新的高增益观测器,进而利用现有文献中的集值映射和迭代设计方法,构造了一个量化输出反馈控制器,最后利用循环小增益定理和动态量化策略,得到了保证闭环系统所有状态有界性且输出最终任意小的充分性条件.     

基于观测器的模糊时滞系统指数稳定的一种设计方法

研究了一类模糊时滞系统的指数稳定问题.首先利用T-S模型对非线性不确定性时滞系统进行建模,在此基础上设计了基于观测器的模糊状态反馈控制器,通过巧妙选取Lyapunov函数给出了模糊闭环时滞系统的条件及稳定裕度且模糊反馈增益和模糊观测器增益可通过求解线性矩阵不等式获得.     

单边Lipschitz离散非线性系统的降阶观测器设计

本文对一类非线性系统的降阶观测器的设计问题进行研究, 基于单边Lipschitz条件和二次内积有界条件, 证明全阶观测器渐近稳定的充分条件也适用于降阶观测器, 即当满足全阶观测器的条件时, 降阶观测器也是渐近稳定的. 最后给出一个数值算例, 说明了所提结果的有效性.     

一类不确定随机非线性系统的采样扩张状态观测器设计与观测误差的收敛性分析

实际系统中普遍存在各种干扰和不确定性因素,并且对控制系统的性能造成负面影响,因此设计对干扰和不确定性具有优异估计性能的观测器显得尤为重要.针对一类具有采样输出的不确定随机非线性系统,设计相应的采样扩张状态观测器用于在线估计不可量测状态和影响系统性能的随机总干扰.所估计的随机总干扰包含系统内部未建模动态、统计特性未知的外部有界噪声干扰以及不确定性因素的非线性耦合作用.在每个采样区间内,设计一个输出预估器用于估计实际输出,相应的输出估计值用于采样扩张状态观测器的设计.证明了所设计的采样扩张状态观测器对不可量测状态和随机总干扰的观测误差的均方收敛性.最后,一个具体仿真实例用于证实理论结果.     

Design of observers for nonlinear systems with H ∞ performance analysis

This paper investigates the problem of observer design for nonlinear systems. By using differential mean value theorem, which allows transforming a nonlinear error dynamics into a linear parameter varying system, and based on Lyapunov stability theory, an approach of observer design for a class of nonlinear systems with time‐delay is proposed. The sufficient conditions, which guarantee the estimation error to asymptotically converge to zero, are given. Furthermore, an adaptive observer design for a class of nonlinear system with unknown parameter is considered. A method of H _∞ adaptive observer design is presented for this class of nonlinear systems; the sufficient conditions that guarantee the convergence of estimation error and the computing method for observer gain matrix are given. Finally, an example is given to show the effectiveness of our proposed approaches. Copyright © 2013 John Wiley & Sons, Ltd.     

Robust Observer Design for a Class of Nonlinear Systems Using the System Internal Dynamics Structure

In this paper, an observer design strategy is presented for a class of nonlinear systems with structural uncertainty. The modern geometric approach is exploited to simplify the system structure. Then, based on the Lyapunov direct method, a robust observer is proposed using the system internal dynamics structure and the distribution of the uncertainty structure. The bound on the uncertainty, which is employed in the observer design, is allowed to be nonlinear and have a more general form. Simulation shows that the proposed approach is effective.     

Adaptive output feedback stabilization for nonholonomic systems with strong nonlinear drifts

This paper investigates the design of an output feedback adaptive stabilization controller for a nonholonomic chained system with strong nonlinear drifts, including modeled nonlinear dynamics, unmodeled dynamics, and dynamics modeled with unknown parameters. Also the virtual control directions of the system are unknown. The purpose is to design a nonlinear output feedback switching controller such that the closed loop system is globally asymptotically stable. A novel observer and estimator are introduced for states and parameter estimates, respectively. A constructive procedure of design for an output feedback adaptive controller is given, by using the integrator backstepping approach and based on the proposed observer and parameter estimator. An example is given to show the effectiveness of the proposed scheme.     

High Gain Observers Using an Approximate Observer Normal Form

If one can transform a nonlinear system into observer normal form, it is possible to design an observer with exactly linear error dynamics. Unfortunately, many systems of practical relevance violate the existence conditions of the normal form. This drawback can be circumvented by means of an approximate observer normal form. The actual computation of the associated transformation may still be very difficult. We suggest a nonlinear observer design procedure that avoids this drawback. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Reduced order observer design for nonlinear systems

This work is a geometric study of reduced order observer design for nonlinear systems. Our reduced order observer design is applicable for Lyapunov stable nonlinear systems with a linear output equation and is a generalization of Luenberger’s reduced order observer design for linear systems. We establish the error convergence for the reduced order estimator for nonlinear systems using the center manifold theory for flows. We illustrate our reduced order observer construction for nonlinear systems with a physical example, namely a nonlinear pendulum without friction.     

基于观测器的模糊Delta算子系统的控制器设计

对于非线性模糊系统控制器和观测器的分析和设计,提出一种统一方法。利用Delta域离散T—S模糊模型对非线性系统建模,并基于李雅普诺夫稳定性理论给出模糊状态反馈控制器和观测器的设计策略,将所得结果归结为求解一组线性矩阵不等式。同时结论表明:分离性原理对Delta算子T—S模糊系统仍然成立。所得结果可将现有关于连续和离散T—S模糊系统的相关结论统一于Delta算子框架内。     

Full-order and reduced-order observers for one-sided Lipschitz nonlinear systems using Riccati equations

This paper aims to design full-order and reduced-order observers for one-sided Lipschitz nonlinear systems. The system under consideration is an extension of its known Lipschitz counterpart and possesses inherent advantages with respect to conservativeness. For such system, we first develop a novel Riccati equation approach to design a full-order observer, for which rigorous mathematical analysis is performed. Consequently, we show that the conditions under which a full-order observer exists also guarantee the existence of a reduced-order observer. A design method for the reduced-order observer that is dependent on the solution of the Riccati equation is then presented. The proposed conditions are easily and numerically tractable via standard numerical software. Furthermore, it is theoretically proven that the obtained conditions are less conservative than some existing ones in recent literature. The effectiveness of the proposed observers is illustrated via a simulative example.     

On Observer Design for a Class of Nonlinear Systems Including Unknown Time-Delay

The observer design for nonlinear systems with unknown, bounded, time-varying delays, on both input and state, is still an open problem for researchers. In this paper, a new observer design for a class of nonlinear system with unknown, bounded, time-varying delay was presented. For the proof of the observer stability, a Lyapunov–Krasovskii function was chosen. Sufficient assumptions are provided to prove the practical stability of the proposed observer. Furthermore, the exponential convergence of the observer was proved in the case of a constant time delay. Simulation results were shown to illustrate the feasibility of the proposed strategy.

     

Reduced order observer design for discrete-time nonlinear systems

This work is a geometric study of reduced order observer design for discrete-time nonlinear systems. Our reduced order observer design is applicable for Lyapunov stable discrete-time nonlinear systems with a linear output equation and is a generalization of Luenberger’s reduced order observer design for linear systems. We establish the error convergence for the reduced order estimator for discrete-time nonlinear systems using the center manifold theory for maps. We illustrate our reduced order observer construction for discrete-time nonlinear systems with an example.     

State observers for a class of multi-output nonlinear dynamic systems

This note considers the problem of observer design for a class of multi-output nonlinear systems. A new state observer design methodology for linear time-varying multi-output systems is presented. Furthermore, we show that the same methodology can be extended to a class of multi-output nonlinear systems. Some sufficient conditions for the existence of the proposed observer are obtained, which guarantee that the error of state estimation converges asymptotically to zero. An example is given to demonstrate the effectiveness of the proposed methodology.