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.     

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 via Immersion and Invariance for vision-based leader-follower formation control

The paper introduces a new vision-based range estimator for leader-follower formation control, based upon the Immersion and Invariance (I&I) methodology. The proposed reduced-order nonlinear observer is simple to implement, easy to tune and achieves global asymptotical convergence of the observation error to zero. Observability conditions for the leader-follower system are analytically derived by studying the singularity of the Extended Output Jacobian. The stability of the closed-loop system arising from the combination of the range estimator and an input-state feedback controller is proved by means of Lyapunov arguments. Simulation experiments illustrate the theory and show the effectiveness of the proposed designs.     

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。     

一般非线性相似组合大系统的渐近观测器

利用现代微分几何方法和分析法相结合,给出了由一般非线性控制系统经非线性互联而成的相似组合大系统渐近观测器存在的充分条件.     

浅析Observer模式在GIS软件设计中的应用

面向对象方法仅仅从问题域的离散抽象很难达到高内聚和低耦合,设计模式的出现和广泛应用为解决这个问题提供了有效的方法.探讨了Observer模式的基本原理以及在GIS软件设计中的应用,并在具体实践中做了有益尝试.实践证明了设计模式在改善软件的灵活性和适应性方面所发挥的积极作用.     

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 design for the Lur'e differential inclusion system with Markovian jumping parameters

This article deals with the observer design for the Lur'e differential inclusion system with Markovian jumping parameters. The set-valued mapping in the system is assumed to be upper semi-continuous, closed, convex, bounded and monotone. The full-order and reduced-order observers are designed to make the corresponding error systems exponentially stable in the mean square, respectively. The criteria are given to guarantee the existence of both full-order and reduced-order observers. The rotor system is considered as an example to show the validity of the proposed method.     

Observer design for range and orientation identification

A reduced-order globally convergent observer to estimate the depth of an object projected on the image plane of a camera is presented, assuming that the object is planar or has a planar surface and the orientation of the plane is known. A locally convergent observer can be obtained when the plane unit normal is unknown, and the latter is estimated together with the depth of the object. The observer exploits the image moments of the object as measured features. The estimation is achieved by rendering attractive and invariant a manifold in the extended state space of the system and the observer. The problem is reduced to the solution of a system of partial differential equations. The solution of the partial differential equations can become a difficult task, hence it is shown that this issue can be resolved by adding to the observer an output filter and a dynamic scaling parameter.     

Control strategy for state and input observer design

In this note, an alternative to classical methods for observer design is discussed, based on a dual control approach: it is indeed highlighted how an observer (at least approximate) can be obtained for a system by designing a control law for an auxiliary copy of this system, so that it tracks the system output. An important ingredient in this approach is the use of high-gain in the control design. The strategy is illustrated by various examples, including the case of unknown input reconstruction.     

Observer design and output feedback stabilization for linear singular time-delay systems with unknown inputs

The design of a functional observer and reduced-order observer with internal delay for linear singular timedelay systems with unknown inputs is discussed. The sufficient conditions of the existence of observers, which are normal linear time-delay systems, and the corresponding design steps are presented via linear matrix inequality(LMI). Moreover, the observer-based feedback stabilizing controller is obtained. Three examples are given to show the effectiveness of the proposed methods.     

Observer design and output feedback stabilization for linear singular time-delay systems with unknown inputs

The design of a functional observer and reduced-order observer with internal delay for linear singular timedelay systems with unknown inputs is discussed. The sufficient conditions of the existence of observers, which are normal linear time-delay systems, and the corresponding design steps are presented via linear matrix inequality（LMI）. Moreover, the observer-based feedback stabilizing controller is obtained. Three examples are given to show the effectiveness of the proposed methods.     

A finite element approach for multiphase fluid flow in porous media

The main scope of this work is to carry out a mathematical framework and its corresponding finite element (FE) discretization for the partially saturated soil consolidation modelling in presence of an immiscible pollutant. A multiphase system with the interstitial voids in the grain matrix filled with water (liquid phase), water vapour and dry air (gas phase) and with pollutant substances, is assumed. The mathematical model addressed in this work was developed in the framework of mixture theory considering the pollutant saturation-suction coupling effects. The ensuing mathematical model involves equations of momentum balance, energy balance and mass balance of the whole multiphase system. Encouraging outcomes were achieved in several different examples.     

Observer design for nonlinear discrete‐time systems: Immersion and dynamic observer error linearization techniques

This paper focuses on the observer design for nonlinear discrete‐time systems by means of nonlinear observer canonical form. At first, sufficient and necessary conditions are obtained for a class of autonomous nonlinear discrete‐time systems to be immersible into higher dimensional observer canonical form. Then a method called dynamic observer error linearization is developed. By introducing a dynamic auxiliary system, the augmented system is shown to be locally equivalent to the generalized observer form, whose nonlinear terms contain auxiliary states and output of the system. A constructive algorithm is also provided to obtain the state coordinate transformation. These results are an extension of their counterparts of nonlinear continuous‐time systems to nonlinear discrete‐time systems (Syst. Control Lett. 1986; 7 :133–142; SIAM. J. Control Optim. 2003; 41 :1756–1778; Int. J. Control 2004; 77 :723–734; Automatica 2006; 42 :321–328; IEEE Trans. Automat. Control 2007; 52 :83–88; IEEE Trans. Automat. Control 2004; 49 :1746–1750; Automatica 2006; 42 :2195–2200; IEEE Trans. Automat. Control 1996; 41 :598–603; Syst. Control Lett. 1997; 31 :115–128). Copyright © 2009 John Wiley & Sons, Ltd.     

带有大输出时滞的ODE–热方程级联系统的观测器设计

为了估计系统的状态并补偿输出时滞,本文提出一种新颖的观测器设计方法应用在常微分方程(ODE)-热方程级联系统中.不同于传统观测器的设计方法,该方法的核心思想是将大时滞划分为若干段小时滞,再设计一串级联的子观测器逐步地估计系统的状态.这种方法的优势在于对于大时滞仍有效.本文通过backstepping-like方法实现了原系统与目标系统的等价变换,结合Lyapunov-Krasovskii方法和线性矩阵不等式理论,得到了误差系统指数稳定的结果.最后,通过仿真实例验证了级联观测器的有效性.     

On Observer Design for Nonlinear Caputo Fractional‐Order Systems

The observer design problem for integer‐order systems has been the subject of several studies. However, much less interest has been given to the more general fractional‐order systems, where the fractional‐order derivative is between 0 and 1. In this paper, a particular form of observers for integer‐order Lipschitz, one‐sided Lipschitz and quasi‐one‐sided Lipschitz systems, is extended to the fractional‐order calculus. Then, the obtained states estimates are used for an eventual feedback control, and the separation principle is tackled. The effectiveness of the proposed scheme is shown through simulation for two numerical examples.     

Robust State‐and‐Disturbance Observer Design for Linear Non‐minimum‐phase Systems

When there are external disturbances acting on the system, the conventional Luenberger observer design for state estimation usually results in a biased state estimate. This paper presents a robust state and disturbance observer design that gives both accurate state and disturbance estimates in the face of large disturbances. The proposed robust observer is structurally different from the conventional one in the sense that a disturbance estimation term is included in the observer equation. With this disturbance estimation term, the robust observer design problem is skillfully transformed into a disturbance rejection control problem. We then can utilize the standard H_∞ control design tools to optimize the robust observer between the disturbance rejection ability and noise immune ability. An important advantage of the proposed robust observer is that it applies to both minimum‐phase systems and non‐minimum phase systems.     

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.     

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.     

Adjoint-based optimization of multi-phase flow through porous media – A review

The recovery of oil from subsurface reservoirs often requires the injection of water or gas to maintain reservoir pressure and to displace the oil from injection to production wells. The design of an economically optimal recovery strategy is usually based on ’reservoir simulation’, i.e. large-scale numerical simulation of the flow of multi-phase fluids through strongly heterogeneous porous media with uncertain coefficients. Control of the recovery process is through prescribing time-varying pressures or flow rates in the wells. Efficient methods to optimize the recovery strategy make use of gradients of an economic objective function with respect to the well controls at every time step. These can be obtained efficiently with the aid of adjoint-based techniques. Constraints, in particular those that involve states (reservoir pressures or saturations) or outputs (measured well pressures or rates) require special treatment. Uncertainty in the coefficients can be incorporated through robust optimization over an ensemble of models. The limited controllability of the reservoir states offers scope for reduced-order modeling using techniques like proper orthogonal decomposition. ‘Closed-loop’ optimization can be performed through frequent repetition of the optimization during the producing life of the field in combination with updating the of the model coefficients based on production measurements. Moreover, an emerging technology is the operational use of model-based optimization which requires a combination of long-term and short-term objectives through multi-level optimization strategies.