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.     

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.     

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。     

Observer design for a class of MIMO nonlinear systems

A simple observer is proposed for a large class of MIMO nonlinear systems which includes many physical models. The main characteristic of the proposed observer lies in the easiness of its implementation and calibration. Indeed, the gain of this observer does not necessitate the resolution of any dynamical system and its expression is given. Moreover, its calibration is achieved through the choice of a single parameter. A simulation example is given in order to illustrate the performance of the proposed observer.     

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．     

Observer design for neutral systems with delays and nonlinear perturbations: Delay-dependent design method

In this paper, the problem of the observer-based control for neutral systems with mixed time-varying delay and nonlinear perturbations is investigated. By using a class of novel augmented Lyapunov-Krasovskii functionals, delay dependent stability criteria are proposed to guarantee the stability of the observer-based control systems. In terms of linear matrix inequality techniques, the observer design and maximum allowable delay bound of neutral systems can be obtained. Finally, a numerical example is provided to illustrate the effectiveness of the proposed approach.     

Observer design for a class of multi-input multi-output nonlinear systems

In this article, the problem of state observer design for a class of multi-input multi-output nonlinear systems is considered. Via state transformation and the constructive use of a Lyapunov function, the new observer design approach is addressed by introducing a parameter ? in the observer. Some sufficient conditions are given which guarantee the estimation error to asymptotically converge to zero under adaptive conditions. An example is included to illustrate the method.     

Observer design for systems with time-delayed states

Recently, the conditions of observers that can estimate directly Kx(t) for an arbitrarily given K, and that are free of the effect of time delayed states of the system, are formulated. This paper points out that, because of the equivalence in formulation, the existing conditions for unknown input observers can be used to establish directly a new set of sufficient conditions for that recent observer. This new set of sufficient conditions is much simpler, and therefore much more useful and significant, than the sufficient conditions derived in that recent paper. This new set of sufficient conditions also reveals some basic mistakes of that recent paper. In addition, this paper reveals the severe restrictiveness of this new set of conditions and proposes a fundamentally new observer design formulation that can relax that set of conditions significantly.     

Observer design for time-varying systems

The state estimation problem is considered for linear time–varying continuous systems with non–lexicographic–fixed observability basis. A two–stage design strategy is presented for constructing observers for this class of systems. At the first stage, by augmenting the given system with an auxiliary system, the original system is transformed to a new augmented model whose observability indices are lexicographic–fixed. A specific augmentation scheme is proposed in order to find this auxiliary system. At the second stage, a design procedure is given to construct minimum–order observers for the augmented system by utilizing the new input and output information. The canonical transformation technique is also employed to simplify the design procedure. Finally, with the help of a simple reverse transformation, solutions to the original problem arc obtained. An example is also given to illustrate the design techniques.     

Observer design for stochastic-parameter systems

Constant-gain linear observer design is utilized to reconstruct the state vector of stochastic systems with both multiplicative and additive noises. It is shown that if the system model is mean square stable, then it is very easy to design an effective estimation scheme     

带线性输出的一般非线性系统的观测器设计

一般非线性系统的观测器设计一直是控制理论研究的重点.本文针对一类带线性输出的一般非线性系统的观测器设计问题,通过微分中值定理,给出了观测器的一般形式.然后利用构造“观测器Lyapunov函数”,提出了一种较为宽松的一般非线性系统观测器设计方法,并证明其渐进稳定性.针对两个典型的一般非线性系统和双线性系统的分析说明了所给算法是可行的.最后,通过对一个单摆系统的观测器构造方法可以看出该算法是简单的且是易于实现的.     

Observer with linear error dynamics for nonlinear multi-output systems

Based upon nonlinear state coordinate transformations and a condensed dual Brunovský form for multi-output systems, a method for designing nonlinear state observers with linear error dynamics is presented. Necessary and sufficient conditions are provided for identifying the class of nonlinear systems for which state observers with linear error dynamics can be obtained.     

Observer design for systems with multivariable monotone nonlinearities

Globally convergent observers are designed for a class of systems with multivariable nonlinearities. The approach is to represent the observer error system as the feedback interconnection of a linear system and a state-dependent multivariable nonlinearity. We first extend an earlier design (Automatica 37 (12) (2001) 1923) to multivariable nonlinearities, satisfying an analog of the scalar nondecreasing property. Next, we exploit the structure of the nonlinearity to relax the positive real restriction on the linear part of the observer error system. This relaxed design renders the feasibility conditions less restrictive, and widens the applicability of the observer, as illustrated with examples. Finally, output nonlinearities are studied and the design is extended to be adaptive in the presence of unknown parameters.     

Observer design for continuous-time dynamical systems

We review the main design techniques of state observer design for continuous-time dynamical systems, namely algorithms which reconstruct online the full information of a dynamical process on the basis of partially measured data. Starting from necessary conditions for the existence of such asymptotic observers, we classify the available methods depending on the detectability/observability assumptions they require. We show how each class of observer relies on transforming the system dynamics in a particular normal form which allows the design of an observer, and how each observability condition guarantees the invertibility of its associated transformation and the convergence of the observer. Finally, some implementation aspects and open problems are briefly discussed.     

Observer design for discrete systems with unknown exogenous inputs

A design procedure is developed for determining optimal discrete observers for estimating system states and unknown exogenous system inputs. This procedure is based on augmenting a standard system observer with an input model. The augmented model is then transformed into the discrete z-domain to determine relevant input/output transfer function matrices. The transfer function matrices are used to develop transfer function relationships between unknown exogenous inputs and the observer estimate of these inputs. It is shown that the optimal observer gains can be determined by implementing the observer as a Fisher filter. An example of the procedure is demonstrated with a third-order point-mass tracking filter     

Observer design for linear processes model with implicit nonlinear output map

Linear dynamical models with nonlinear output maps can represent a wide range of industrial processes. In particular, in many applications the output maps are defined in terms of an implicit function. In this context, it is necessary to design an observer which does not require to invert explicitly the output map in order to obtain the estimated output. The proposed approach considers this particular requirement, a nonlinear perturbation term associated to the dynamic part, characterized in terms of a Lipschitz constant, and a continuous differentiable output map. The stability of the non-linear error dynamic is analysed by transforming the error dynamic into a Linear Parameter Varying (LPV) system. Two representative examples, i.e. neutralization process and conductivity estimation, illustrate the main features of the design process and the performance obtained with the proposed observer.     

Observer design for generalized state space systems with unknown inputs

The following four major aspects for the observer design problem for generalized state space systems with unknown inputs are resolved: Necessary and sufficient conditions for the problem to have a solution, the order of the minimal observer, the properties of the closed-loop system (separation principle) and general analytical expressions of the minimal order observer matrices. All above results are first in the field.     

Lurie广义系统基于观测器的控制器设计

研究了Lurie广义系统基于状态观测器的控制器设计问题.通过使用Lyapunov稳定性理论,线性矩阵不等式方法,分别给出了状态反馈控制器和观测器的设计方法,并建立了分离原理,进而得到了基于观测器的控制器设计方法.所得结论对广义系统理论本身的发展和实际应用都有非常重要的意义.最后给出了仿真实例.