State estimation for discrete-time markov jump linear systems based on orthogonal projective theorem

In this paper, state estimation problem for discrete-time Markov jump linear systems is considered. Based on orthogonal projective theorem, a novel suboptimal algorithm for state estimate of discrete-time Markov jump linear systems in the sense of minimum mean square error estimate is proposed. The proposed suboptimal algorithm is recursive and finite-dimensionally computable. Computer simulations are carried out to evaluate the performance of the proposed suboptimal algorithm.     

Robust and efficient map-to-image registration with line segments

This work investigates map-to-image registration for planar scenes in the context of robust parameter estimation. Registration is posed as the problem of estimating a projective transformation which optimally aligns transformed model line segments from a map with data line segments extracted from an image. Matching and parameter estimation is solved simultaneously by optimizing an objective function which is based on M-estimators, and depends on overlap and the weighted orthogonal distance between transformed model segments and data segments. An extensive series of registration experiments was conducted to test the performance of the proposed parameter estimation algorithm. More than 200 000 registration experiments were run with different objective functions for 12 aerial images and randomly corrupted maps distorted by randomly selected projective transformations. Received: 10 August 2000 / Accepted: 29 January 2001     

Near-optimal state estimation for interconnected systems

A new algorithm is proposed for estimating the state of a nonlinear stochastic system when only noisy observations of the state are available. The state estimation problem is formulated as a modal-trajectory, maximum likelihood estimation problem. The resulting minimization problem is analogous to the nonlinear tracking problem in optimal control theory. By viewing the system as an interconnection of lower-dimension subsystems and applying the so-called ε-coupling technqiue, which originated in the study of sensitivity of control systems to parameter variations, a near-optimal state estimation algorithm is derived which has the properties that all computations can be performed in parallel at the subsystem level and only linear equations need be solved. The principal attraction of the method is that significant reductions in the computational requirements relative to other approximate algorithms can be achieved when the system is large-dimensional.     

带有乘性过程噪声和模式观测时滞离散马氏跳线性系统的状态估计

研究受乘性过程噪声干扰的离散马氏跳线性系统状态估计问题. 系统可得到的观测包括两部分: 模式观测和输出观测, 其中模式观测受到固定时滞的影响. 利用贝叶斯定理及所得到的一些结果, 提出一种新颖的最小均方误差意义下次优状态估计算法. 该次优算法是回归的, 并且不随着时间增加而加重计算存储负荷. 通过计算机仿真来评估所提出次优算法的性能, 仿真结果验证了该算法的优越性.

     

A geometric approach for the analysis and computation of the intrinsic camera parameters

The authors of this paper adopted the projected characteristics of the absolute conic in terms of the Pascal's theorem to propose an entirely new camera calibration method based on purely geometric thoughts. The use of this theorem in the geometric algebra framework allows us to compute a projective invariant using the conics of only two images which expressed using brackets helps us to set enough equations to solve the calibration problem. The method requires restricted controlled camera movements. Our method is less sensitive to noise as the Kruppa's-equation-based methods. Experiments with simulated and real images confirm that the performance of the algorithm is reliable.     

Active fault tolerant control for switched positive linear systems

The main aim of this paper is to design an active fault tolerant controller for switched positive linear systems. A theorem is proved for fault and state estimation of switched positive linear systems in terms of matrix inequality by considering average dwell‐time approach. By utilizing the theorem results, not only a fast and exact estimation of fault and state is obtained but also the positivity of state estimation is ensured. The feasibility problem is solved by formulating it into a special sequential optimization problem subject to LMI constraints. Based on the fault estimation information, an observer‐based fault tolerant control guaranties the stability and positivity of the closed‐loop system. Finally, a practical example including a data communication network is presented to illustrate the efficiency of the proposed method.     

网联车辆协同巡航系统快速滚动时域状态估计

考虑云平台监控下的网联车辆协同自动巡航控制(CACC)系统,提出一种快速滚动时域估计方法.采用网联车队纵向动力学模型描述网联车辆CACC系统,降低网联车辆CACC系统的状态能观性要求.再应用块概念设计滚动时域估计算法的噪声块结构,压缩滚动时域估计问题的优化变量个数,从而减少其在线计算量.进一步,应用李雅普诺夫稳定性定理证明估计误差系统的渐近稳定性.最后以5车网联车队系统仿真验证所提算法的有效性.     

Design of Adaptive Block Backstepping Controllers with Perturbations Estimation for Nonlinear State‐Delayed Systems in Semi‐Strict Feedback Form

This paper is an extended study of an existing block backstepping control scheme designed for a class of perturbed multi‐input systems with multiple time‐varying delays to solve regulation problems, where the time‐varying delays must be linear with state variables. A new control scheme is proposed in this research where all the unknown multiple time‐varying delay terms in the dynamic equations can be nonlinear state functions in non‐strict feedback form, and the upper bounds of the time‐delays as well as their derivatives need not to be known in advance. Another improvement is to further alleviate the problem of “explosion of complexity,” i.e., to reduce the number of time derivatives of virtual inputs that the designers have to compute in the design of controllers. This is done by utilizing an existent derivative estimation algorithm to estimate the perturbations in the designing of proposed controllers. Adaptive mechanisms are also embedded in the controllers so that the upper bounds of perturbations and perturbation estimation errors are not required to be known beforehand. The resultant controlled systems guarantee asymptotic stability in accordance with the Lyapunov stability theorem. Finally, a numerical example and a practical application are demonstrated to verify the merits and feasibility of the proposed control scheme.     

Optimal Estimation of A Class of Linear Time‐Delay Uncertain Systems

The state estimation problem is investigated for a class of linear uncertain systems with state and noise delay. The optimal one‐step prediction algorithm is presented by introducing a fictitious noise. The predictor is designed based on the projection formula in Hilbert space and has the same dimensions as the original systems. The error covariance consists of two coupled Riccati‐type difference equations. The optimal filter and fixed‐lag smoother are provided based on the predictor. A numerical example is given to show the effectiveness of the proposed approach.     

A new block algorithm for full-rank solution of the Sylvester-observer equation

A new block algorithm for computing a full rank solution of the Sylvester-observer equation arising in state estimation is proposed. The major computational kernels of this algorithm are: 1) solutions of standard Sylvester equations, in each case of which one of the matrices is of much smaller order than that of the system matrix and (furthermore, this small matrix can be chosen arbitrarily), and 2) orthogonal reduction of small order matrices. There are numerically stable algorithms for performing these tasks including the Krylov-subspace methods for solving large and sparse Sylvester equations. The proposed algorithm is also rich in Level 3 Basic Linear Algebra Subroutine (BLAS-3) computations and is thus suitable for high performance computing. Furthermore, the results on numerical experiments on some benchmark examples show that the algorithm has better accuracy than that of some of the existing block algorithms for this problem.     

基于粒子群优化方法的电力系统状态向量估计模型

电力系统状态向量估计是电力系统能量管理系统的重要组成部分;在电力系统实时监控中,传统的基于最小二乘法的状态向量估计方法,存在估计值与实际电力系统中的参数值相差较大的问题,基于此提出了一种适用于电力系统实时监测的有效状态估计模型;该模型采用了一种基于直角坐标系的加权最小二乘法,由一组与测量量和状态变量相关的非线性方程组描述,使用预测-校正迭代技术求解状态估计器模型;利用粒子群算法优化同步相量测量单元(phasor measurements unit,PMU)仪表的分配,增强了算法的有效性;该模型被应用于IEEE14总线和IEEE-30总线测试系统;结果表明,与传统算法相比,所开发的电力系统状态向量估计模型在执行时间、准确性和迭代次数方面均有明显的优势,所提出的估计模型对于实时监控应用具有很好的应用前景.     

State estimation scheme for nonlinear dynamical systems based on the stochastic approximation

An algorithm for the state estimation of multivariable nonlinear dynamic systems with noisy nonlinear observation systems is investigated on the basis of stochastic approximation procedure.Using an extended version of Dvoretzky's theorem, we derive a sufficient condition that estimation error converges to zero, both in the mean square and with probability one for noise-free multivariable dynamical systems. We then show that our estimation procedure makes the estimation error bounded in the mean square norm for noisy dynamical systems. Some numerical examples are presented for the illustration of the approach mentioned above.     

一种由未定标图象估计三维射影不变量的新算法

本文提出了一种由未定标图象估计三维射不变量的新算法。实验结果表明了本算法的有效性。     

Using Algorithms of Decomposition for Computation of Linear Stochastic Models

The mathematical apparatus of decomposition is used to solve the problem of analysis and computation of stiff stochastic systems of differential equations. A theorem substantiating the adequacy of a solution obtained is formulated and an algorithm of computation of stiff stochastic systems by the method of depression of equations is given.     

带有随机通信时滞的状态估计

研究了测量值不带时间戳的网络控制系统的最优状态估计问题. 当最大的随机时滞界是一步滞后时, 对可能存在的乱序测量提出新的测量模型. 基于每一时刻收到的所有测量值的平均值构造估计器以保证不稳定网络控制系统的估计器是线性无偏的及估计误差协方差一致有界, 并通过求解离散黎卡提方程得到估计器增益. 在无偏性及误差协方差一致有界的意义下保证估计器是最优的. 最后给出仿真实例验证了该算法的有效性.     

A new orthogonal series approach to state-space analysis and identification

The contribution of this paper is two-fold. First, it introduces a new orthogonal series approach to the state-space analysis of linear time-invariant systems. This approach yields explicit expressions for the state and output vector coefficient matrices. These expressions only involve the multiplication of matrices of small dimensions. No algebraic system of equations needs to be solved, and therefore no inversion of large matrices is required here, as compared to other known techniques. The second contribution consists of using this new orthogonal series technique to solve the state-space identification problem. It is shown that by appropriately manipulating the aforementioned state-space analysis results, an algorithm is derived which yields the state-space system matrix A. This algorithm gives a new outlook and a better insight into the state-space identification problem.     

Solution of two-point-boundary-value problems by generalized orthogonal polynomials and application to optimal control of lumped and distributed parameter systems

A set of generalized orthogonal polynomials (GOPs) that can represent all types of orthogonal polynomial and non-orthogonal Taylor series are first introduced to solve dynamic state equations with two-point-boundary conditions. The basic idea is that any orthogonal polynomial function can be expressed as a power series, and vice versa. The operational matrix for the integration of the generalized orthogonal polynomials is thus derived. Using the special characteristics of these generalized orthogonal polynomials, the state equation of the two-point-boundary-value problem is thus reduced to that of an initial-value problem. This effective approach can be applied to solve the optimal control of a lumped or distributed parameter system. The computational algorithm, in conjunction with the recursive formula, is much simpler and easier than that for conventional individual orthogonal polynomials.     

Event-based input and state estimation for linear discrete time-varying systems

In this paper, the joint input and state estimation problem is considered for linear discrete-time stochastic systems. An event-based transmission scheme is proposed with which the current measurement is released to the estimator only when the difference from the previously transmitted one is greater than a prescribed threshold. The purpose of this paper is to design an event-based recursive input and state estimator such that the estimation error covariances have guaranteed upper bounds at all times. The estimator gains are calculated by solving two constrained optimisation problems and the upper bounds of the estimation error covariances are obtained in form of the solution to Riccati-like difference equations. Special efforts are made on the choices of appropriate scalar parameter sequences in order to reduce the upper bounds. In the special case of linear time-invariant system, sufficient conditions are acquired under which the upper bound of the error covariance of the state estimation is asymptomatically bounded. Numerical simulations are conducted to illustrate the effectiveness of the proposed estimation algorithm.