Identification of errors-in-variables state space models with observation outliers based on minimum covariance determinant

In this paper, a subspace system identification algorithm for the errors-in-variables (EIV) state space models subject to observation noise with outliers has been developed. By using the minimum covariance determinant (MCD) estimator, the outliers have been identified and deleted. Then the classical EIV subspace system identification algorithms have been applied to estimate the parameters of the state space models. In order to solve the MCD problem for the EIV state space models, a random search algorithm has been proposed. A Monte-Carlo simulation results demonstrate the effectiveness of the proposed algorithm.     

一种新的基于线性EIV模型的鲁棒估计算法

提出了一种新的基于线性EIV模型的鲁棒估计算法——鲁棒扩充算法．该算法从结构化数据区域出发,逐渐扩充模型数据集,并不断更新模型参数的估计,直至找到所有模型数据．在每次迭代中,使用C-Step方法对集合进行调整,从而保证了算法的鲁棒性．同时,提出了关于粗差数据和结构化数据分布的结构化密度假设,结合Mean Shift算法,完成对算法的初始位置选取．仿真结果表明,该算法可以有效地处理含有多个结构和大量离群样本的混杂数据,与现有算法相比,具有更强的鲁棒性和更高的精度．     

Feature‐Preserving Surface Reconstruction From Unoriented,Noisy Point Data

We propose a robust method for surface mesh reconstruction from unorganized, unoriented, noisy and outlier‐ridden 3D point data. A kernel‐based scale estimator is introduced to estimate the scale of inliers of the input data. The best tangent planes are computed for all points based on mean shift clustering and adaptive scale sample consensus, followed by detecting and removing outliers. Subsequently, we estimate the normals for the remaining points and smooth the noise using a surface fitting and projection strategy. As a result, the outliers and noise are removed and filtered, while the original sharp features are well preserved. We then adopt an existing method to reconstruct surface meshes from the processed point data. To preserve sharp features of the generated meshes that are often blurred during reconstruction, we describe a two‐step approach to effectively recover original sharp features. A number of examples are presented to demonstrate the effectiveness and robustness of our method.     

Consolidation of Low‐quality Point Clouds from Outdoor Scenes

The emergence of laser/LiDAR sensors, reliable multi‐view stereo techniques and more recently consumer depth cameras have brought point clouds to the forefront as a data format useful for a number of applications. Unfortunately, the point data from those channels often incur imperfection, frequently contaminated with severe outliers and noise. This paper presents a robust consolidation algorithm for low‐quality point data from outdoor scenes, which essentially consists of two steps: 1) outliers filtering and 2) noise smoothing. We first design a connectivity‐based scheme to evaluate outlierness and thereby detect sparse outliers. Meanwhile, a clustering method is used to further remove small dense outliers. Both outlier removal methods are insensitive to the choice of the neighborhood size and the levels of outliers. Subsequently, we propose a novel approach to estimate normals for noisy points based on robust partial rankings, which is the basis of noise smoothing. Accordingly, a fast approach is exploited to smooth noise, while preserving sharp features. We evaluate the effectiveness of the proposed method on the point clouds from a variety of outdoor scenes.     

Robust identification of MISO neuro‐fractional‐order Hammerstein systems

This paper introduces a multiple‐input–single‐output (MISO) neuro‐fractional‐order Hammerstein (NFH) model with a Lyapunov‐based identification method, which is robust in the presence of outliers. The proposed model is composed of a multiple‐input–multiple‐output radial basis function neural network in series with a MISO linear fractional‐order system. The state‐space matrices of the NFH are identified in the time domain via the Lyapunov stability theory using input‐output data acquired from the system. In this regard, the need for the system state variables is eliminated by introducing the auxiliary input‐output filtered signals into the identification laws. Moreover, since practical measurement data may contain outliers, which degrade performance of the identification methods (eg, least‐square–based methods), a Gaussian Lyapunov function is proposed, which is rather insensitive to outliers compared with commonly used quadratic Lyapunov function. In addition, stability and convergence analysis of the presented method is provided. Comparative example verifies superior performance of the proposed method as compared with the algorithm based on the quadratic Lyapunov function and a recently developed input‐output regression‐based robust identification algorithm.     

Robust identification for nonlinear errors-in-variables systems using the EM algorithm

This article presents a robust identification approach for nonlinear errors-in-variables (EIV) systems contaminated with outliers. In this work, the measurement noise is modelled using the t-distribution, instead of the traditional Gaussian distribution, to mitigate the effect of the outliers. The heavier tails of the t-distribution, through the adjustable degrees of freedom, is used to account for noise and outliers concomitantly. Further, to avoid the intricacies related to the direct nonlinear identification, we propose to approximate the nonlinear EIV dynamics using multiple local ARX models and aggregating them using an exponential weighting strategy. The parameters of the local models and weighting parameters are estimated using the expectation maximization (EM) algorithm, under the framework of the maximum likelihood estimation (MLE). The studies with simulated numerical examples and an experiment on a multi-tank system demonstrate the superiority of the proposed method.     

A random least-trimmed-squares identification algorithm

The Least-trimmed-squares (LTS) estimator is a well known robust estimator in terms of protecting the estimate from the outliers. Its high computational complexity is however a problem in practice. In this paper, we propose a random LTS algorithm which has a low computational complexity that can be calculated a priori as a function of the required error bound and the confidence interval. Moreover, if the number of data points goes to infinite, the algorithm becomes a deterministic one that converges to the true LTS in some probability sense.     

Output‐based disturbance rejection control for 1‐D anti‐stable Schrödinger equation with boundary input matched unknown disturbance

In this paper, we are concerned with the output feedback control design for a system (plant) described by a boundary controlled anti‐stable one‐dimensional Schrödinger equation. Our output measure signals are the displacements at both side. An untraditional infinite‐dimensional disturbance estimator is developed to estimate the disturbance. Based on the estimator, we propose a state observer that is exponentially convergent to the original system and then design a stabilizing control law consisting of two parts: The first part is to compensate the disturbance by using its approximated value and the second part is to stabilize the observer system by applying the classical backstepping approach. The resulting closed‐loop system is shown to be exponentially stable with guaranteeing that all internal systems are uniformly bounded. An effective output‐based disturbance rejection control algorithm is concluded. An application, namely, a cascade of ODE–wave systems, is investigated by the developed control algorithm. Numerical experiments are carried out to illustrate the effectiveness of the proposed control law. Copyright © 2017 John Wiley & Sons, Ltd.     

Outliers, inliers and the generalized least trinuned squares estimator in system identification

The least trimmed squares estimator (LTS) is a well known robust estimator in terms of protecting the estimate from the outliers. Its high computational complexity is however a problem in practice. We show that the LTS estimate can be obtained by a simple algorithm with the complexity O( N In N) for large N, where N is the number of measurements. We also show that though the LTS is robust in terms of the outliers, it is sensitive to the inliers. The concept of the inliers is introduced. Moreover, the Generalized Least Trimmed Squares estimator (GLTS) together with its solution are presented that reduces the effect of both the outliers and the inliers.     

Design of UDE‐based controllers from their two‐degree‐of‐freedom nature

The control algorithm based on the uncertainty and disturbance estimator (UDE) is a robust control strategy and has received wide attention in recent years. In this paper, the two‐degree‐of‐freedom nature of UDE‐based controllers is revealed. The set‐point tracking response is determined by the reference model, whereas the disturbance response and robustness are determined by the error feedback gain and the filter introduced to estimate the uncertainty and disturbances. It is also revealed that the error dynamics of the system is determined by two filters, of which one is determined by the error feedback gain and the other is determined by the filter introduced to estimate the uncertainty and disturbances. The design of these two filters are decoupled in the frequency domain. Moreover, after introducing the UDE‐based control, the Laplace transform can be applied to some time‐varying systems for analysis and design because all the time‐varying parts are lumped into a signal. It has been shown that, in addition to the known advantages over the time‐delay control, the UDE‐based control also brings better performance than the time‐delay control under the same conditions. Design examples and simulation results are given to demonstrate the findings. Copyright © 2010 John Wiley & Sons, Ltd.     

Multi‐sensor track‐to‐track fusion via linear minimum variance sense estimators

An integrated approach that consists of sensor‐based filtering algorithms, local processors, and a global processor is employed to describe the distributed fusion problem when several sensors execute surveillance over a certain area. For the sensor tracking systems, each filtering algorithm utilized in the reference Cartesian coordinate system is presented for target tracking, with the radar measuring range, bearing, and elevation angle in the spherical coordinate system (SCS). For the local processors, each track‐to‐track fusion algorithm is used to merge two tracks representing the same target. The number of 2‐combinations of a set with N distinct sensors is considered for central track fusion. For the global processor, the data fusion algorithms, simplified maximum likelihood (SML) estimator and covariance matching method (CMM), based on linear minimum variance (LMV) estimation fusion theory, are developed for use in a centralized track‐to‐track fusion situation. The resulting global fusers can be implemented in a parallel structure to facilitate estimation fusion calculation. Simulation results show that the proposed SML estimator has a more robust capability of improving tracking accuracy than the CMM and the LMV estimators. Copyright © 2008 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Adaptive model predictive control of nonlinear systems with state‐dependent uncertainties

This paper studies adaptive model predictive control (AMPC) of systems with time‐varying and potentially state‐dependent uncertainties. We propose an estimation and prediction architecture within the min‐max MPC framework. An adaptive estimator is presented to estimate the set‐valued measures of the uncertainty using piecewise constant adaptive law, which can be arbitrarily accurate if the sampling period in adaptation is small enough. Based on such measures, a prediction scheme is provided that predicts the time‐varying feasible set of the uncertainty over the prediction horizon. We show that if the uncertainty and its first derivatives are locally Lipschitz, the stability of the system with AMPC can always be guaranteed under the standard assumptions for traditional min‐max MPC approaches, while the AMPC algorithm enhances the control performance by efficiently reducing the size of the feasible set of the uncertainty in min‐max MPC setting. Copyright © 2017 John Wiley & Sons, Ltd.     

Multi‐targets localization and elliptical circumnavigation by multi‐agents using bearing‐only measurements in two‐dimensional space

In order to enable the multi‐agents to elliptically circumnavigate the multi‐targets in more complex environment, we propose a geometric center estimator and an elliptical circumnavigation controller in two‐dimensional space by only employing bearing measurements without knowing the target's position and velocity. The stability of the algorithm is proved for both stationary targets and dynamic targets. Finally, a series of numerical simulations is presented to verify the correctness of the algorithm both in ideal networks and in networks with communication delays.     

A fuzzy median‐of‐intercept straight‐line algorithm for use in noisy images

Recently, a crisp robust median‐of‐intercept (MI) straight‐line fitting algorithm was devised for use in image‐processing applications. The algorithm is specifically designed for use in noisy images when the input data is corrupted with both noise and outliers. In this article we describe a fuzzy MI algorithm whose performance is significantly better than the original crisp algorithm. In addition, the new algorithm is fast; its computational complexity being only marginally greater than the original MI algorithm. © 2003 Wiley Periodicals, Inc.     

Noise‐Adaptive Shape Reconstruction from Raw Point Sets

We propose a noise‐adaptive shape reconstruction method specialized to smooth, closed shapes. Our algorithm takes as input a defect‐laden point set with variable noise and outliers, and comprises three main steps. First, we compute a novel noise‐adaptive distance function to the inferred shape, which relies on the assumption that the inferred shape is a smooth submanifold of known dimension. Second, we estimate the sign and confidence of the function at a set of seed points, through minimizing a quadratic energy expressed on the edges of a uniform random graph. Third, we compute a signed implicit function through a random walker approach with soft constraints chosen as the most confident seed points computed in previous step.     

Outliers, inliers and the generalized least trimmed squares estimator in system identification

The least trimmed squares estimator (LTS) is a well known robust estinaator in terms of protecting the estimatefrom the outliers. Its high computational complexity is however a problem in practice. We show that the LTS estimate can be obtained by a simple algorithm with the complexity O( N In N) for large N, where N is the number of measurements. We also showthat though the LTS is robust in terms of the outliers, it is sensitive to the inliers. The concept of the inliers is introduced. Moreover, the Generalized Least Trimmed Squares estimator (GLTS) together with its solution are presented that reduces the effect of both the outliers and the inliers.     

Fault‐Tolerant Control Based on Augmented State Estimator and PDF

A new fault‐tolerant control based on augmented state estimator and probability density function (PDF) is proposed for a stochastic distribution system (SDS) with time‐delay and additive fault. First, a system model based on a PDF with the additive fault is constructed by using square‐root rational B‐spline neural networks. Second, an augmented system is obtained by converting the additive fault as an auxiliary state variable. In this framework, a robust augmented state estimator is designed to estimate the original states and the additive fault simultaneously. Then, based on the obtained estimation of fault, a delay‐dependent fault‐tolerant control is designed to compensate the fault. Finally, the numerical simulations show the effectiveness of the proposed method.     

Robust disturbance rejection for repetitive control systems with time‐varying nonlinearities

This paper presents a disturbance‐rejection method for a modified repetitive control system with a nonlinearity. Taking advantage of stable inversion, an improved equivalent‐input‐disturbance (EID) estimator that is more relaxed for system design is developed to estimate and cancel out the influence of the disturbance and nonlinearity in the low‐frequency domain. The high‐frequency influence is filtered owning to the low‐pass nature of the linear part of the closed‐loop system. To avoid the restrictive commutative condition and choose a Lyapunov function of a more general form, a new design algorithm, which takes into account the relation between the feedback control gains and the observer and improved EID estimator gains, is developed for the nonlinear system. Furthermore, comparisons with the generalized extended‐state observer (GESO) and conventional EID methods are conducted. A clear relation between the developed estimator and the GESO is also clarified. Finally, simulations show the effectiveness and the advantage of the developed method.     

A two‐stage sampling for robust feature matching

For any visual feature‐based SLAM (simultaneous localization and mapping) solutions, to estimate the relative camera motion between two images, it is necessary to find “correct” correspondence between features extracted from those images. Given a set of feature correspondents, one can use a n‐point algorithm with robust estimation method, to produce the best estimate to the relative camera pose. The accuracy of a motion estimate is heavily dependent on the accuracy of the feature correspondence. Such a dependency is even more significant when features are extracted from the images of the scenes with drastic changes in viewpoints and illuminations and presence of occlusions. To make a feature matching robust to such challenging scenes, we propose a new feature matching method that incrementally chooses a five pairs of matched features for a full DoF (degree of freedom) camera motion estimation. In particular, at the first stage, we use our 2‐point algorithm to estimate a camera motion and, at the second stage, use this estimated motion to choose three more matched features. In addition, we use, instead of the epipolar constraint, a planar constraint for more accurate outlier rejection. With this set of five matching features, we estimate a full DoF camera motion with scale ambiguity. Through the experiments with three, real‐world data sets, our method demonstrates its effectiveness and robustness by successfully matching features (1) from the images of a night market where presence of frequent occlusions and varying illuminations, (2) from the images of a night market taken by a handheld camera and by the Google street view, and (3) from the images of a same location taken daytime and nighttime.     

Robust control under worst‐case uncertainty for unknown nonlinear systems using modified reinforcement learning

Reinforcement learning (RL) is an effective method for the design of robust controllers of unknown nonlinear systems. Normal RLs for robust control, such as actor‐critic (AC) algorithms, depend on the estimation accuracy. Uncertainty in the worst case requires a large state‐action space, this causes overestimation and computational problems. In this article, the RL method is modified with the k‐nearest neighbor and the double Q‐learning algorithm. The modified RL does not need the neural estimator as AC and can stabilize the unknown nonlinear system under the worst‐case uncertainty. The convergence property of the proposed RL method is analyzed. The simulations and the experimental results show that our modified RLs are much more robust compared with the classic controllers, such as the proportional‐integral‐derivative, the sliding mode, and the optimal linear quadratic regulator controllers.