Recursive design of finite-time convergent observers for a class of time-varying nonlinear systems

This paper considers the problem of designing globally finite-time convergent observers for a class of nonlinear systems with time-varying and output-dependent coefficients, which make the existing design approaches inapplicable. To solve this problem, a bottom-up design approach is first employed to recursively construct a finite-time convergent observer with time-varying coefficients for the nominal system. Then, using the homogeneous domination approach, we scale the finite-time convergent observer with an appropriate choice of gain for the original nonlinear system satisfying a Hölder condition. In addition, we show that the Hölder condition imposed on the nonlinearities can be removed for nonlinear systems with bounded trajectories.     

Recursive filtering for nonlinear systems subject to measurement outliers

In this paper,an innovative recursive filtering algorithm(RFA)is proposed for a class of nonlinear systems(NSs)subject to multiplicative noises(MNs)and measurem...     

Recursive scaling design for robust global nonlinear stabilization via output feedback

This paper proposes a novel approach to robust backstepping for global stabilization of uncertain nonlinear systems via output feedback. The design procedure developed in this paper is based on the concept of state‐dependent scaling, which handles output‐feedback stabilization problems of strict‐feedback systems with various structures of uncertainties in a unified way. The proposed method is suitable for numerical computation. The theory of the method employs the Schur complements formula instead of Young's inequality and completing the squares. This paper shows a condition of allowable uncertainty size under which an uncertain system is globally stabilized by output feedback. A class of systems is shown to be always globally stabilizable for arbitrarily large nonlinear size of uncertainties. A recursive procedure of robust observer design for such a class of uncertain systems is presented. Copyright © 2000 John Wiley & Sons, Ltd.     

On observer design for nonlinear systems

The main weakness of all control methodologies is the dependency of feedbacks to full state measurements. In practical situations, measuring the states of a given system may fail because sometimes the measurements are impossible and sometimes, possible, but too expensive. Observer design for highly nonlinear dynamics is an important issue, particularly when the locally observable dynamics are not linearly observable. In such circumstances the ability to reduce the system to observable or observer form is key to observer design. This paper provides two observers for nonlinear systems given in Brunovski form. The first observer is a high-gain observer with a classical output injection form, while the second is a high-gain observer with a q-integral path. Finally, the discrete-time implementation of the high-gain observer is discussed in linear matrix inequality framework. A motivating example is shown to highlight the efficacy of the developed observers.     

Backstepping design for time-delay nonlinear systems

The backstepping approach is adapted to the problem of globally uniformly asymptotically stabilizing nonlinear systems in feedback form with a delay arbitrarily large in the input. The strategy of design relies on the construction of a Lyapunov-Krasovskii functional. Continuously differentiable control laws are constructed.     

非线性时滞系统的观测器设计

研究了一类满足Lipschitz条件的下三角非线性时滞系统的观测器设计问题.通过构造适当的Lyapunov泛函,用递推法给出了使得误差动态系统渐近趋于零的非线性时滞系统的状态观测器.     

Recursive nonlinear observer design: beyond the uniform observability

We propose a recursive design scheme of a state observer for multiple-input-multiple-output, partly lower triangular nonlinear systems. The design begins from the subdynamics far from the output and propagates to the subdynamics close to the output, recalling the backstepping scheme for nonlinear control. The proposed class of systems is fairly general since it includes nonuniformly observable and/or detectable multioutput systems. Error convergence to zero is proved assuming boundedness of inputs a posteriori (i.e., after the design), which is preferable whereas most results in the literature assume the boundedness; a priori (i.e., before the design). A global observer is proposed with the global Lipschitz condition of the system, but without any restriction on the size of Lipschitz coefficient. The Lipschitz condition can be removed when a semiglobal observer is of interest.     

Recursive identification algorithms to design fault detection systems

This paper deals with the recursive identification of the parity space based fault detection systems. We propose two such algorithms that update the eigenstructure after every new measurement with significantly less computational cost. Its immediate application is in the design of adaptive parity space based residual generators. The method improves the fault detection performance against uncertain changes, especially the frequent shifts in operating points, or parameter variations. The algorithms are compared with the existing techniques and applied to the hybrid simulation platform of continuously stirred tank heater.     

Observer design for nonlinear systems with discrete-timemeasurements

This paper focuses on the development of asymptotic observers for nonlinear discrete-time systems. It is argued that instead of trying to imitate the linear observer theory, the problem of constructing a nonlinear observer can be more fruitfully studied in the context of solving simultaneous nonlinear equations. In particular, it is shown that the discrete Newton method, properly interpreted, yields an asymptotic observer for a large class of discrete-time systems, while the continuous Newton method may be employed to obtain a global observer. Furthermore, it is analyzed how the use of Broyden's method in the observer structure affects the observer's performance and its computational complexity. An example illustrates some aspects of the proposed methods; moreover, it serves to show that these methods apply equally well to discrete-time systems and to continuous-time systems with sampled outputs     

Observer design for autonomous discrete-time nonlinear systems

We obtain a necessary and sufficient condition for a discrete-time nonlinear system to be locally state equivalent to the nonlinear observer form. The result looks similar to the continuous counterpart except for the fact that Ad-operation is utilized instead of ad-operation.     

Stabilizing compensator design for uncertain nonlinear systems

An observer-based control scheme is proposed for exponentially stabilizing a class of uncertain nonlinear systems. The control and observer gain expressions given in this paper resemble those used in variable-structure designs but they are continuous in nature resulting in a simple analysis of stability.     

Switching observer design for uncertain nonlinear systems

The problem of designing a switching observer for a finite or infinite set of nonlinear time-varying systems with unknown parameters and/or varying structure is studied in this paper. Under a compactness condition and a Lyapunov detectability assumption, it is shown that a switching observer with asymptotically stable error dynamics can be constructed. Different from the variable structure control method, only a finite number of switches occur before the asymptotic stability is achieved. The Lyapunov direct method is used to construct both the switching gain and the switching index. The special case where the error dynamics becomes exponentially convergent with quadratic Lyapunov detectability is also examined to illustrate the proposed observer design procedure     

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。     

Lipschitz非线性系统观测器设计新方法

考虑了非线性项满足Lipschitz条件的非线性系统观测器设计问题, 利用Lyapunov方法给出了新的判断观测误差稳定性的条件, 并由所给的条件通过求解线性矩阵不等式来设计观测器. 通过算例与其它方法进行的比较, 说明了所提方法的有效性.     

不确定随机非线性系统自适应观测器设计

考虑带非参数不确定项的随机非线性系统自适应观测器设计问题.不同于已有结果,系统的不确定项无需满足Lipschitz连续性条件,也不必要仅仅是系统输出的函数.通过设计一个带参数自适应律的非线性观测器来重构系统状态,该观测器结构简单目易于实现.应用Lyapunov稳定性理论和随机微分理论证明该观测器是最终有界的,并且它的界可以通过选取适当的参数进行调节.最后,数值仿真结果表明了该观测器的有效性.     

Reduced-order observer-based control design for nonlinear stochastic systems

In this paper, we investigate the stabilization control design problem of nonlinear stochastic SISO systems in strict-feedback form. By introducing a novel reduced-order observer, an output-feedback-based control is constructively designed, which renders the closed-loop system asymptotically stable in the large when the nonlinearities and stochastic disturbance equal zero at the equilibrium point of the open-loop system, and bounded in probability, otherwise. Besides, the obtained controller preserves the equilibrium point of the open-loop nonlinear system.     

Robust design of stochastic controllers for nonlinear systems

The previous results are generalized on the stabilizing property of a control scheme designed for a class of discrete-time nonlinear stochastic systems. First, the existing controller is made more robust with a prescribed degree of stability by proper modifications. Next, the inherent robustness is illustrated by a design utilizing erroneous noise characteristics. Reconsideration of the stability analysis used allows one to treat a larger class of nonlinear stochastic systems with more general structures     

非线性切换系统基于观测器的容错控制器设计

针对一类具有执行器故障的非线性切换系统,研究基于系统状态估计和故障重构的容错控制问题.首先,在具有平均驻留时间(ADT)的切换信号下,设计一种切换PI观测器作为状态-故障估计器,以达到对系统状态和故障同时渐近估计的目的;其次,基于线性矩阵不等式,给出非线性切换系统观测器存在的充分条件;再次,基于PI观测器给出的状态和故障估计,提出一种非线性切换系统的容错控制器设计方法;最后,以一个电子电路为仿真实例进行分析,验证了所提出方法的可行性和适用性.