基于观测器的非脆弱控制研究及其在混沌系统中的应用

研究了递增二次限制非线性系统中基于观测器的非脆弱控制问题.递增二次限制条件包含很多常见的非线性条件,如Lipschitz,扇形非线性,单边Lispchitz条件,作为特例.针对一类满足递增限制条件的非线性系统,设计了基于观测器的非脆弱控制器.基于线性矩阵不等式方法,建立了闭环控制系统渐近稳定的充分条件.最后,使用Lor...     

针对准单边Lipschitz不确定非线性时滞系统的稳定性分析

研究了一类不确定非线性时滞系统的鲁棒稳定性. 准单边Lipschitz条件被介绍, 并被用于估计非线性向量函数在稳定性分析中的影响. 线性矩阵不等式形式的时滞无关/时滞相关稳定性判据被得到. 此外, 即使系统系数是不稳定的, 这些稳定性判据也是可利用的, 因为未必正定的准单边Lipschitz常数矩阵包含了很多非线性部分的有用信息. 数值实例证实了本文所获结果的有效性.     

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。     

一类非线性系统的函数观测器设计

研究单边Lipschitz非线性系统的函数观测器设计.基于线性矩阵不等式获得了函数观测器增益矩阵存在的条件,然后提出函数观测器增益矩阵的设计方法.通过一个仿真实例,验证所设计的函数观测器不仅能够估计系统的状态,而且可使观测误差快速收敛到零.     

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.     

基于线性矩阵不等式的一类广义系统观测器设计

状态反馈控制能有效进行系统控制,并使其正常工作。由于系统状态的测量具有一定的难度,因此需要设计状态观测器,利用重构的状态进行反馈。针对一类非线性部分满足Lipschitz条件的广义系统,讨论了系统全维观测器和降维观测器的设计问题。首先,根据系统的可观性,提出对广义系统进行两次变换,并将系统变换成易于设计观测器的形式。其次,利用系统的变换式对系统的两种观测器进行设计,通过Lyapunov稳定性理论给出观测器的状态估计误差系统稳定且误差收敛于零的充分条件。考虑到观测器增益矩阵求解的盲目性,利用Schur补引理给出了两种观测器存在的充分条件,并简化了增益矩阵的求解过程。最后,给出数值算例,求解出两种观测器的增益矩阵,证明了观测器设计的可行性。该研究为类似系统观测器的构建提供了设计方法。     

一类非线性切换系统的观测器设计

研究了一类切换规则为时间依赖型的非线性切换系统的观测器设计问题．分别在切换序列已知与平均驻留时间已知的情况下利用线性矩阵不等式（LMI）给出了非线性项满足Lipschitz条件的切换系统的观测器增益求解方法,并给出了观测器设计步骤．最后给出仿真算例说明了本文方法的有效性．     

中立型非线性不确定时滞系统的控制器设计

研究了一类中立型非线性不确定时滞系统的稳定性分析和状态观测器设计问题,系统包含状态时滞和非线性不确定性,基于Lyapunov稳定性理论,给出了该类时滞系统在非线性不确定性满足增益有界的条件下状态观测器存在的充分条件,并通过线性矩阵不等式(LMI)方法构造得出基于状态观测器的动态输出反馈控制器,最后给出一个数值算例验证了本文结果的有效性.     

一类非线性系统的自适应观测器

研究一类非线性系统的观测器设计方法, 这类非线性系统满足 Lipschitz 条件且含有未知参数. 提出了全状态自适应观测器设计的新方法. 构造的观测器能保证状态估计误差及参数估计误差渐近收敛于零. 文中给出数值例验证了观测器的有效性.     

Sensor fault estimation for Lipschitz nonlinear systems in finite-frequency domain

In this study, the problem of sensor fault estimation observer design for Lipschitz nonlinear systems with finite-frequency specifications is investigated. First, the sensor fault is considered as an auxiliary state vector and an augmented system is established. Then, by transforming the nonlinear error dynamics into a linear parameter varying system, a sufficient condition for the observer-error system with a finite-frequency H_∞ performance is derived in terms of linear matrix inequalities (LMIs). Based on the obtained condition, novel nonlinear observers are designed to simultaneously estimate the system states and the fault signals and attenuate the disturbances in the finite-frequency domain. The proposed design method can provide less restrictive LMI conditions and get a better disturbance-attenuation performance when the frequency ranges of disturbances are known beforehand. A numerical example is given to show the effectiveness and superiority of the new results.     

Observers for Lipschitz nonlinear systems

This paper presents some fundamental insights into observer design for the class of Lipschitz nonlinear systems. The stability of the nonlinear observer for such systems is not determined purely by the eigenvalues of the linear stability matrix. The correct necessary and sufficient conditions on the stability matrix that ensure asymptotic stability of the observer are presented. These conditions are then reformulated to obtain a sufficient condition for stability in terms of the eigenvalues and the eigenvectors of the linear stability matrix. The eigenvalues have to be located sufficiently far out into the left half-plane, and the eigenvectors also have to be sufficiently well-conditioned for ensuring asymptotic stability. Based on these results, a systematic computational algorithm is then presented for obtaining the observer gain matrix so as to achieve the objective of asymptotic stability     

Adaptive nonlinear observer for state and unknown parameter estimation in noisy systems

This paper proposes a novel adaptive observer for Lipschitz nonlinear systems and dissipative nonlinear systems in the presence of disturbances and sensor noise. The observer is based on an H_∞ observer that can estimate both the system states and unknown parameters by minimising a cost function consisting of the sum of the square integrals of the estimation errors in the states and unknown parameters. The paper presents necessary and sufficient conditions for the existence of the observer, and the equations for determining observer gains are formulated as linear matrix inequalities (LMIs) that can be solved offline using commercially available LMI solvers. The observer design has also been extended to the case of time-varying unknown parameters. The use of the observer is demonstrated through illustrative examples and the performance is compared with extended Kalman filtering. Compared to previous results on nonlinear observers, the proposed observer is more computationally efficient, and guarantees state and parameter estimation for two very broad classes of nonlinear systems (Lipschitz and dissipative nonlinear systems) in the presence of input disturbances and sensor noise. In addition, the proposed observer does not require online computation of the observer gain.     

Nonlinear observer design for one‐sided Lipschitz systems with time‐varying delay and uncertainties

This paper investigates the problem of state observer design for a class of nonlinear uncertain dynamical systems with interval time‐varying delay and the one‐sided Lipschitz condition. By constructing the novel Lyapunov–Krasovskii functional while utilizing the free‐weighting matrices approach, the one‐sided Lipschitz condition and the quadratic inner‐bounded condition, novel sufficient conditions, which guarantee the observer error converge asymptotically to zero, are established for a class of nonlinear dynamical systems with interval time‐varying delay in terms of the linear matrix inequalities. The computing method for observer gain matrix is given. Finally, two examples illustrate the effectiveness of the proposed method. Copyright © 2016 John Wiley & Sons, Ltd.     

Observer‐based finite‐time stabilization for discrete‐time switched singular systems with quadratically inner‐bounded nonlinearities

This paper discusses the observer‐based finite‐time stabilization for discrete‐time switched singular systems with quadratically inner‐bounded nonlinear terms. Firstly, based on the Luenberger‐like observer, by using the average dwell time approach, sufficient conditions are proposed to make closed‐loop systems be regular, be causal, as having a unique solution, and be uniformly finite‐time bounded. Then, a new linear matrix inequality sufficient condition for the existence of an observer‐based controller is obtained by using certain matrix decoupling techniques, and the controller is designed. In this paper, the conditions proposed not only give the observer‐based controller design methods but also guarantee the existence and uniqueness of solution for the systems. Since the quadratically inner‐bounded nonlinearities are more general than Lipschitz nonlinearities and one‐sided Lipschitz nonlinearities, compared with previous works, the proposed controller design methods in this paper are also more general than the existing ones. Finally, numerical examples are provided to illustrate the effectiveness of the methods proposed in this paper.     

Robust Fractional-Order Proportional-Integral Observer for Synchronization of Chaotic Fractional-Order Systems

In this paper, we propose a robust fractional-order proportional-integral (FOPI) observer for the synchronization of nonlinear fractional-order chaotic systems. The convergence of the observer is proved, and sufficient conditions are derived in terms of linear matrix inequalities (LMIs) approach by using an indirect Lyapunov method. The proposed FOPI observer is robust against Lipschitz additive nonlinear uncertainty. It is also compared to the fractional-order proportional (FOP) observer and its performance is illustrated through simulations done on the fractional-order chaotic Lorenz system.