Fal函数的改进及3种新型非线性扩张状态观测器

首先分析现有fal函数和传统非线性扩张状态观测器中存在的6类问题,提出一种固定时间收敛的fal函数,其收敛速度快于传统fal函数,且收敛时间上界与初始误差无关;然后,分别设计基于新型fal函数的非线性扩张状态观测器、指数收敛非线性扩张状态观测器和全新结构的固定时间收敛非线性扩张状态观测器;最后,通过仿真验证这3种新型的非线性扩张状态观测器的估计总误差相对于传统非线性扩张状态观测器分别减少15.4%、16.9%和93.8%,对应的被控状态总误差分别减少13.6%、30.4%和78.3%.     

Parametric eigenvalue-eigenvector assignment in reduced-order observer design

The design of reduced-order state observers for linear multivariable systems is considered. The procedure used is based on the assignment of prespecified sets of eigenvalues and associated eigenvectors to the observer model, whereby the state estimation error is effectively governed. It is shown, in particular, that the restrictions on the assignable eigenvectors are removed when the number of system outputs equals or exceeds half the number of state variables. Moreover, with the outputs in excess of half the state variables, some design parameters remain unaffected by the assignment of both sets of eigenvalues and eigenvectors. A certain part of these additional parameters can be adjusted to alleviate the impact of misalignment between the system and the observer initial states. The remaining part contributes to the identification of the observer matrices—other than the dynamical coefficient matrix. The one-to-one correspondence between the observability of the system and the eigenvalue assignability of the observer in the framework of this approach is demonstrated.     

Using set invariance to design robust interval observers for discrete‐time linear systems

Based on interval and invariant set computation, an interval version of the Luenberger state observer for uncertain discrete‐time linear systems is proposed in this work. This new interval observer provides a punctual estimation of the state vector and guaranteed bounds on the estimation error. An off‐line and an on‐line approach to characterize, in a guaranteed way, the estimation error are introduced. Compared with the existing approaches, the proposed interval observer design method is not restrictive in terms of required assumptions, complexity, and on‐line computation time. Furthermore, the convergence issue of the estimation error is well established and to reduce the conservatism of the estimated state enclosure induced by the bounded additive state disturbance and noise measurement, an H_∞ method to compute the optimal observer gain is proposed. The performance of the proposed state estimation approach are highlighted on different illustrative examples.     

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.     

光电跟踪系统临界探测概率研究

光电跟踪系统的估计性能随着探测概率的下降而降低,是否存在一个临界探测概率,当跟踪系统的实际探测概率高于临界探测概率时,跟踪系统统计意义下的估计误差协方差对任意估计初值均收敛是跟踪系统设计时的一个关键问题。本文证明了跟踪系统临界探测概率的存在性,并且给出了临界探测概率的一组上下界,其上界被描述成一个非线性矩阵不等式(NMI)的最优解,其下界仅与跟踪系统状态转移矩阵的特征值有关。进一步利用摄动线性化方法给出了求解临界探测概率上界的一种迭代线性矩阵不等式(ILMI)算法,并且对跟踪系统在三种标准测试场景中的临界探测概率上界进行了仿真求解,仿真结果表明:当跟踪系统的探测概率高于50%时,其统计意义下的估计误差协方差对任意估计初值均收敛,这为跟踪系统探测概率的设计提供了理论依据。     

一类非线性系统的自适应观测器

This paper investigates the means to design the ob- server for a class of nonlinear systems with Lipschitz conditions and unknown parameters.A new design approach of full-order state adaptive observer is proposed.The constructed observer could guarantee the error of state and the error of parameter estimation to asymptotically converge to zero.Furthermore,a numerical example is provided to verify the effectiveness of the observer.     

An observer for systems with nonlinear output map

A nonlinear observer, with the feedback gain weighted by the sensitivity of the output with respect to the state, is developed for systems with nonlinear output map. The observer can be obtained from the extended Kalman filter by a special choice of time-varying weighting matrices. It is shown that the estimation error dynamics are asymptotically stable and a region of attraction is derived. The observer is applied to the top blown converter process for estimating the content of impurities in the liquid metal. Using plant data from the converter at SSAB Oxelösund AB, the observer is shown to provide accurate estimates of the carbon content.     

Parameter-dependent state observer design for affine LPV systems

In this paper, the design of a parameter-dependent state observer that allows to estimate the state of an affine linear parameter-varying (LPV) system is investigated. The observer has the property of being parameter-dependent since the corresponding state space matrices are scheduled using an interpolation method. Moreover, the stability of the estimation error is based on the existence of an affine parameter-dependent Lyapunov function. The main contribution of this paper is that the problem of the observer design and the existence of such a Lyapunov function is interpreted as a flexible LMI feasibility condition. Some illustrative examples are presented at the end of this paper.     

Design of linear observers for a class of linear hybrid systems

This paper deals with the design of linear observers for a class of linear hybrid systems. Such systems are composed of continuous-time and digital substates and possess, in general, coupling dynamics between both substates. Two observer prototypes based on the prediction error are proposed. The first is based on the observation of an extended discrete system at sampling instants. The discrete extended state is composed of the sampled values of the continuous substate at sampling instants and the digital substate. The estimation of the continuous substate in between sampling instants is made by using the plant parametrization and the sampled prediction error at the preceding sampling instant. The continuous-time state estimates are reinitialized at each new sampling instant by taking values from the corresponding components of the discretized substate of the observer of the auxiliary discrete extended system. The second observer prototype estimates the continuous-time substate for all time from initial conditions which are taken only when the estimation algorithm starts. The observer involves feedback information of the current observation error, that of the preceding sampling instant and that associated with the estimation of the discrete system. As a result, the discontinuities of the estimated substate at sampling instants, which typically occur with the use of the first prototype, are not present in this observation scheme. The exponential convergence to zero of both prediction and observation errors may be ensured under observability and detectability assumptions Furthermore, prescribed pole placement of the state estimation error is achieved under observability of the discrete extended plant. Also, prescribed pole placement of the combined dynamics of the extended plant and observation error can be obtained. For that purpose, the extended hybrid plant is assumed to be controllable when the linear control input is generated from measurements of the state observation. in both observation prototypes.     

On the stability of the continuous-time Kalman filter subject to exponentially decaying perturbations

This paper details the stability analysis of the continuous-time Kalman filter dynamics for linear time-varying systems subject to exponentially decaying perturbations. It is assumed that estimates of the input, output, and matrices of the system are available, but subject to unknown perturbations which decay exponentially with time. It is shown that if the nominal system is uniformly completely observable and uniformly completely controllable, and if the state, input, and matrices of the system are bounded, then the Kalman filter built using the perturbed estimates is a suitable state observer for the nominal system, featuring exponentially convergent error dynamics.     

Observers for systems with nonlinearities satisfying incremental quadratic constraints

We consider the problem of designing observers to asymptotically estimate the state of a system whose nonlinear time-varying terms satisfy an incremental quadratic inequality that is parameterized by a set of multiplier matrices. Observer design is reduced to solving linear matrix inequalities for the observer gain matrices. The proposed observers guarantee exponential convergence of the state estimation error to zero. In addition to considering a larger class of nonlinearities than previously considered, this paper unifies earlier related results in the literature. The results are illustrated by application to several examples.     

Optimal bilinear observers for bilinear state-space models by interaction matrices

This paper formulates optimal bilinear observers for bilinear state-space models. Observers in bilinear form, as opposed to other nonlinear forms, are required to develop an extension of observer/Kalman filter identification for simultaneous identification of a bilinear state-space model and an associated bilinear observer from noisy input–output measurements. The paper establishes the relationship between the bilinear observer gains and the interaction matrices which are used to convert the original bilinear state-space model to a form that simplifies the identification of such a model. Techniques to find the interaction matrices are developed. In the absence of noises, these matrices produce the gains of the fastest converging observer. In the presence of noises, they minimise the state estimation error in the same manner as a standard steady-state Kalman filter. Numerical examples illustrate both the theoretical and computational aspects of the proposed algorithms.     

一种新的基于遗忘因子的递推子空间辨识算法

针对工业系统中广泛存在的时变特性, 提出一种新的递推子空间辨识算法, 实现对系统状态空间模型的在线递推估计. 为更好地跟踪系统时变特性, 研究基于遗忘因子的输入输出数据矩阵构造机制, 以提高递推算法的收敛速度; 针对算法中奇异值分解的求解问题, 将梯度型算法引入基于遗忘因子的状态子空间跟踪中, 实现对广义能观测矩阵的估计, 避免了子空间近似带来的估计有偏性; 该算法计算简单有效, 且对初值具有更高的鲁棒性; 最后给出该递推算法的性能分析, 理论证明其收敛性, 并通过仿真实例验证算法的有效性.     

基于RBF神经网络观测器的非线性系统鲁棒故障检测方法

针对一类仿射非线性动态系统，提出一种基于网络非线性观测器的鲁棒故障检测与隔离的新方法，采用ＲＢＦ神经网络逼近观测器系统中的非线性项，提高了状态估计的精度，证明了状态估计误差稳定且渐近收敛到零；同时提出了一种新的网络权值调整指标方法，提高了神经网络故障分类器的泛化能力，从而保证该方法对监测系统的建模 外部扰动具有良好的鲁棒性。     

Observer forms for perspective systems

The estimation of three-dimensional position information from two-dimensional images in computer vision systems can be formulated as a state estimation problem for a nonlinear perspective dynamic system. The multi-output state estimation problem has been treated by several authors using methods for nonlinear observer design. This paper shows that a perspective system can be transformed to two observer forms, and provides constructive methods for arriving at the transformations. These observer forms lead to straightforward observer designs. First, it is shown that, using an output transformation, the system admits an observer form which leads to an observer with linear error dynamics. A second observer design is based on a time-scaled block triangular form. Both designs assume a commonly used observability condition. The designs are demonstrated in simulation.     

激光陀螺单轴旋转惯导系统多位置对准技术研究

激光陀螺单轴旋转惯导系统初始对准精度受陀螺漂移和加速度计零位的限制,为了减少对准误差,对多位置对准技术进行了研究。给出了单轴旋转惯导系统误差方程,利用奇异值分解的方法,对多位置对准时的系统各状态变量的可观测性进行分析,利用卡尔曼滤波仿真研究了多位置对准过程中方位失准角估计误差收敛情况,系统地分析了卡尔曼滤波器参数P0、...     

Quantum Random Walks in One Dimension

This letter treats the quantum random walk on the line determined by a 2 × 2 unitary matrix U. A combinatorial expression for the mth moment of the quantum random walk is presented by using 4 matrices, P, Q, R and S given by U. The dependence of the mth moment on U and initial qubit state is clarified. A new type of limit theorems for the quantum walk is given. Furthermore necessary and sufficient conditions for symmetry of distribution for the quantum walk is presented. Our results show that the behavior of quantum random walk is striking different from that of the classical ramdom walk. PACS: 03.67.Lx; 05.40.Fb; 02.50.Cw     

A state observer for continuous oscillating systems under intrinsic pulse-modulated feedback

A static gain observer for linear continuous plants with intrinsic pulse-modulated feedback is analyzed. The purpose of the observer is to asymptotically drive the state estimation error to zero and synchronize the sequence of pulse modulation instants estimated by the observer with that of the plant. Conditions on the observer gain matrix locally stabilizing the observer error along an arbitrary periodic plant solution are derived and illustrated by simulation for the case of pulsatile testosterone regulation.     

Simultaneous state and output disturbance estimations for a class of switched linear systems with unknown inputs

The paper considers the issues of state estimation and output disturbance reconstruction for a class of switched linear systems with unknown inputs. A singular switched system is derived from the original switched system by taking the output disturbance as a part of a new extended state vector. For the constructed singular switched system, a robust sliding-mode switched observer which can not only estimate the states of original switched system but also reconstruct output disturbances is proposed, where the switching of the observer is synchronous with that of the switched system. A sufficient condition is provided to guarantee the existence of the switched observer by the feasibility of an optimisation problem with linear matrix inequality constraint, and the corresponding switching signal with average dwell time is designed such that the convergence of the estimation error system is proven to be exponential. Based on the state estimation of singular switched system, the methods of state estimation and output disturbance reconstruction of original switched system are proposed. Finally, the simulation results confirm the predicted performance of the proposed methods.