本文为两类非线性系统建立了全局指数观测器存在的充分条件：(i) 具有全局渐近稳定紧集的系统类，以及 (ii) 在开集上演化的系统类。在第一类中，在附加条件下，导出的连续时间观测器还导致鲁棒全局采样数据指数观测器的构造。给出了两个一般结果应用的说明性例子，一个是具有单调非线性的系统，另一个是恒化器系统。
英文摘要：
This paper develops sufficient conditions for the existence of global exponential observers for two classes of nonlinear systems: (i) the class of systems with a globally asymptotically stable compact set, and (ii) the class of systems that evolve on an open set. In the first class, the derived continuous-time observer also leads to the construction of a robust global sampled-data exponential observer, under additional conditions. Two illustrative examples of applications of the general results are presented, one is a system with monotone nonlinearities and the other is the chemostat system.
In this paper we are interested in the problem of state observation of state-affine nonlinear systems. Our main contribution is to propose a globally exponentially convergent observer that requires only the necessary assumption of observability of the system. To the best of the authors' knowledge this is the first time such a result is reported in the literature.
Global Exponential Sampled-Data Observers for Nonlinear Systems with Delayed Measurements
Laboratoire GREYC CNRS-ENSICAEN（GREYC实验室）；Technical University of Crete（克里特理工大学）；Centre National de la Recherche Scientifique, CNRS-EECI SUPELEC（法国国家科学研究中心）
Western University（西安大略大学）；University of Quebec in Outaouais（魁北克大学乌塔韦校区）；Lakehead University（湖首大学）
This paper deals with the simultaneous estimation of the attitude, position and linear velocity for vision-aided inertial navigation systems. We propose a nonlinear observer on $SO(3)\times \mathbb{R}^{15}$ relying on body-frame acceleration, angular velocity and (stereo or monocular) bearing measurements of some landmarks that are constant and known in the inertial frame. Unlike the existing local Kalman-type observers, our proposed nonlinear observer guarantees almost global asymptotic stability and local exponential stability. A detailed uniform observability analysis has been conducted and…
In this work we solve the position-aided 3D navigation problem using a nonlinear estimation scheme. More precisely, we propose a nonlinear observer to estimate the full state of the vehicle (position, velocity, orientation and gyro bias) from IMU and position measurements. The proposed observer does not introduce additional auxiliary states and is shown to guarantee semi-global exponential stability without any assumption on the acceleration of the vehicle. The performance of the observer is shown, through simulation, to overcome the state-of-the-art approach that assumes negligible accelerati…
This paper deals with the problem of full state estimation for vehicles navigating in a three dimensional space. We assume that the vehicle is equipped with an Inertial Measurement Unit (IMU) providing body-frame measurements of the angular velocity, the specific force, and the Earth's magnetic field. Moreover, we consider available sensors that provide partial or full information about the position of the vehicle. Examples of such sensors are those which provide full position measurements (e.g., GPS), range measurements (e.g., Ultra-Wide Band (UWB) sensors), inertial-frame bearing measurement…
Western University（韦仕敦大学）；Lakehead University（湖首大学）
This paper considers the problem of simultaneous estimation of the attitude, position and linear velocity for vehicles navigating in a three-dimensional space. We propose two types of hybrid nonlinear observers using continuous angular velocity and linear acceleration measurements as well as intermittent landmark position measurements. The first type relies on a fixed-gain design approach based on an infinite-dimensional optimization, while the second one relies on a variable-gain design approach based on a continuous-discrete Riccati equation. For each case, we provide two different observers…
We study the output feedback exponential stabilization for a 1-d wave PDE with dynamic boundary. With only one measurement, we construct an infinite-dimensional state observer to trace the state and design an estimated state based controller to exponentially stabilize the original system. This is an essentially important improvement for the existence literature [Ö. Morgül, B.P. Rao and F. Conrad, IEEE Transactions on Automatic Control, 39(10) (1994), 2140-2145] where two measurements including the high order angular velocity feedback were adopted. When a control matched nonlinear internal unce…
An exponential Luenberger dynamical observer is proposed to estimate the state of a general class of nonautonomous semilinear parabolic equations. The result can be applied to the case where the output is given by state measurements taken at a finite number of spatial points, that is, to the case where our sensors are a finite number of delta distributions. The output injection operator is explicit and the derivation of the main result involves the decomposition of the state space into a direct sum of two oblique components depending on the set of sensors. Simulations are presented as an appli…
The paper is devoted to the observability study of a dynamic system, which describes the vibrations of an elastic beam with an attached rigid body and distributed control actions. The mathematical model is derived using Hamilton's principle in the form of the Euler-Bernoulli beam equation with hinged boundary conditions and interface condition at the point of attachment of the rigid body. It is assumed that the sensors distributed along the beam provide output information about the deformation in neighborhoods of the specified points of the beam. Based on the variational form of the equations …
Zhejiang University（浙江大学）；Ningbo University（宁波大学）；Ningbo Artificial Intelligence Institute, Shanghai Jiao Tong University（上海交通大学宁波人工智能研究院）；Huzhou Institute of Zhejiang University（浙江大学湖州研究院）
In this paper, we propose a novel nonlinear observer based on neural networks, called neural observer, for observation tasks of linear time-invariant (LTI) systems and uncertain nonlinear systems. In particular, the neural observer designed for uncertain systems is inspired by the active disturbance rejection control, which can measure the uncertainty in real-time. The stability analysis (e.g., exponential convergence rate) of LTI and uncertain nonlinear systems (involving neural observers) are presented and guaranteed, where it is shown that the observation problems can be solved only using t…
