State estimation for stochastic time‐varying multisensor systems with multiplicative noises: Centralized and decentralized data fusion

In this paper, the state estimation problems, including filtering and one‐step prediction, are solved for uncertain stochastic time‐varying multisensor systems by using centralized and decentralized data fusion methods. Uncertainties are considered in all parts of the state space model as multiplicative noises. For the first time, both centralized and decentralized estimators are designed based on the regularized least‐squares method. To design the proposed centralized fusion estimator, observation equations are first rewritten as a stacked observation. Then, an optimal estimator is obtained from a regularized least‐squares problem. In addition, for decentralized data fusion, first, optimal local estimators are designed, and then fusion rule is achieved by solving a least‐squares problem. Two recursive equations are also obtained to compute the unknown covariance matrices of the filtering and prediction errors. Finally, a three‐sensor target‐tracking system is employed to demonstrate the effectiveness and performance of the proposed estimation approaches.     

Robust face tracking control of a mobile robot using self‐tuning Kalman filter and echo state network

This paper presents a novel design of face tracking algorithm and visual state estimation for a mobile robot face tracking interaction control system. The advantage of this design is that it can track a user's face under several external uncertainties and estimate the system state without the knowledge about target's 3D motion‐model information. This feature is helpful for the development of a real‐time visual tracking control system. In order to overcome the change in skin color due to light variation, a real‐time face tracking algorithm is proposed based on an adaptive skin color search method. Moreover, in order to increase the robustness against colored observation noise, a new visual state estimator is designed by combining a Kalman filter with an echo state network‐based self‐tuning algorithm. The performance of this estimator design has been evaluated using computer simulation. Several experiments on a mobile robot validate the proposed control system. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

自校正解耦信息融合Wiener状态估值器

对含未知噪声方差阵的多传感器系统,用现代时间序列分析方法.基于滑动平均(MA)新息模型的在线辨识和求解相关函数矩阵方程组,可得到估计噪声方差阵估值器,进而在按分量标量加权线性最小方差最优信息融合则下,提出了自校正解耦信息融合Wiener状态估值器.它的精度比每个局部自校正Wiener状态估值器精度高.它实现了状态分量的解耦局部Wiener估值器和解耦融合Wiener估值器.证明了它的收敛性,即若MA新息模型参数估计是一致的,则它将收敛于噪声统计已知时的最优解耦信息融合Wiener状态估值器,因而它具有渐近最优性.一个带3传感器的目标跟踪系统的仿真例子说明了其有效性.     

Stochastic Optimal Design for Unknown Linear Discrete‐Time System Zero‐Sum Games in Input‐Output form Under Communication Constraints

In this paper, stochastic optimal strategy for unknown linear discrete‐time system quadratic zero‐sum games in input‐output form with communication imperfections such as network‐induced delays and packet losses, otherwise referred to as networked control system (NCS) zero‐sum games, relating to the H_∞ optimal control problem is solved in a forward‐in‐time manner. First, the linear discrete‐time zero sum state space representation is transformed into a linear NCS in the state space form after incorporating random delays and packet losses and then into the input‐output form. Subsequently, the stochastic optimal approach, referred to as adaptive dynamic programming (ADP), is introduced which estimates the cost or value function to solve the infinite horizon optimal regulation of unknown linear NCS quadratic zero‐sum games in the presence of communication imperfections. The optimal control and worst case disturbance inputs are derived based on the estimated value function in the absence of state measurements. An update law for tuning the unknown parameters of the value function estimator is derived and Lyapunov theory is used to show that all signals are asymptotically stable (AS) and that the estimated control and disturbance signals converge to optimal control and worst case disturbances, respectively. Simulation results are included to verify the theoretical claims.     

Distributed resilient estimation over sensor networks for nonlinear time‐delayed systems with stochastic perturbations

This paper is concerned with the distributed resilient estimation problem for a class of nonlinear time‐delayed systems subject to stochastic perturbations. The plant and the measurements are disturbed by two Gaussian white stochastic processes with known statistical information, respectively. In addition, a resilient estimator is designed for each node by means of the parameter uncertainties and Bernoulli‐distributed random variables. Then, a novel exponential‐bounded performance index is put forward to measure the disturbance rejection level of the distributed estimators against the external disturbances and the impact of the initial values. A new vector dissipation definition including multiple vectors of energy storage functions is established to deal with the time‐delay estimation error dynamics. Within the framework of local performance analysis inspired by this new definition of vector dissipation, sufficient conditions in terms of recursive linear matrix inequalities are constructed for each node to guarantee the desirable performance index. Next, a local optimization problem subject to a set of recursive linear matrix inequalities is presented for each node to minimize the upper bound in the performance index, where the calculations can be conducted on every node in a distributed manner and the estimator gains are also calculated. Finally, an illustrative simulation example is provided to verify the applicability of the proposed estimators.     

Development of moving window state and parameter estimators under maximum likelihood and Bayesian frameworks

Estimation of slowly varying model parameters/unmeasured disturbances is of paramount importance in process monitoring, fault diagnosis, model based advanced control and online optimization. The conventional approach to estimate drifting parameters is to artificially model them as a random walk process and estimate them simultaneously with the states. However, this may lead to a poorly conditioned problem, where the tuning of the random walk model becomes a non-trivial exercise. In this work, the moving window parameter estimator of Huang et al. [1] is recast as a moving window maximum likelihood (ML) estimator. The state can be estimated within the window using any recursive Bayesian estimator. It is assumed that, when the model parameters are perfectly known, the innovation sequence generated by the chosen Bayesian estimator is a Gaussian white noise process and is further used to construct a likelihood function that treats the model parameters as unknowns. This leads to a well conditioned problem where the only tuning parameter is the length of the moving window, which is much easier to select than selecting the covariance of the random walk model. The ML formulation is further modified to develop a maximum a posteriori (MAP) cost function by including arrival cost for the parameter. Efficacy of the proposed ML and MAP formulations has been demonstrated by conducting simulation studies and experimental evaluation. Analysis of the simulation and experimental results reveals that the proposed moving window ML and MAP estimators are capable of tracking the drifting parameters/unmeasured disturbances fairly accurately even when the measurements are available at multiple rates and with variable time delays.     

A STABLE ON‐LINE SELF‐TUNING OPTIMAL PID CONTROLLER FOR A CLASS OF UNKNOWN SYSTEMS

In this paper, a novel self‐tuning method of optimal PID control laws is proposed for both continuous‐time systems and discrete‐time systems. The controlled plant is assumed to be unknown except the system order (or system delay) and the direction of transmitting control input. Through the minimization of PID gains subject to the Lyapunov stability based reaching condition, the tuning of the three PID control gains is transformed to solve the inequality constraint optimization problem. An unknown SISO nonlinear system subject to a unit step input, and the tracking control problem of the piezoelectric actuator (PZA) with unknown dynamics are simulated. The simulation results show that the excellent tracking performance can be achieved.     

Optimal state estimation using randomly delayed measurements without time stamping

This paper studies an optimal state estimation (Kalman filtering) problem under the assumption that output measurements are subject to random time delays caused by network transmissions without time stamping. We first propose a random time delay model which mimics many practical digital network systems. We then study the so‐called unbiased, uniformly bounded linear state estimators and show that the estimator structure is given based on the average of all received measurements at each time for different maximum time delays. The estimator gains can be derived by solving a set of recursive discrete‐time Riccati equations. The estimator is guaranteed to be optimal in the sense that it is unbiased with uniformly bounded estimation error covariance. A simulation example shows the effectiveness of the proposed algorithm. Copyright © 2013 John Wiley & Sons, Ltd.     

Robust fusion steady‐state filtering for multisensor networked systems with one‐step random delay,missing measurements,and uncertain‐variance multiplicative and additive white noises

The robust fusion steady‐state filtering problem is investigated for a class of multisensor networked systems with mixed uncertainties including multiplicative noises, one‐step random delay, missing measurements, and uncertain noise variances, the phenomena of one‐step random delay and missing measurements occur in a random way, and are described by two Bernoulli distributed random variables with known conditional probabilities. Using a model transformation approach, which consists of augmented approach, derandomization approach, and fictitious noise approach, the original multisensor system under study is converted into a multimodel multisensor system with only uncertain noise variances. According to the minimax robust estimation principle, based on the worst‐case subsystems with conservative upper bounds of uncertain noise variances, the robust local steady‐state Kalman estimators (predictor, filter, and smoother) are presented in a unified framework. Applying the optimal fusion algorithm weighted by matrices, the robust distributed weighted state fusion steady‐state Kalman estimators are derived for the considered system. In addition, by using the proposed model transformation approach, the centralized fusion system is obtained, furthermore the robust centralized fusion steady‐state Kalman estimators are proposed. The robustness of the proposed estimators is proved by using a combination method consisting of augmented noise approach, decomposition approach of nonnegative definite matrix, matrix representation approach of quadratic form, and Lyapunov equation approach, such that for all admissible uncertainties, the actual steady‐state estimation error variances of the estimators are guaranteed to have the corresponding minimal upper bounds. The accuracy relations among the robust local and fused steady‐state Kalman estimators are proved. An example with application to autoregressive signal processing is proposed, which shows that the robust local and fusion signal estimation problems can be solved by the state estimation problems. Simulation example verifies the effectiveness and correctness of the proposed results.     

LINEAR OPTIMAL FEEDBACK AND LOAD‐DECOUPLED CONTROL OF A BUCK DC‐DC CONVERTER

This paper describes a new controller design procedure and tuning method for a PWM buck dc‐dc converter. First, linear optimal feedback is designed using the LQR approach. Then the designed control law is implemented using a PID controller incorporated with a load‐decoupled PD compensator. The PID controller is tuned to achieve the optimal design based on the output error voltage directly, instead of using an estimator. When the proposed PD compensator is used, the converter is robust with respect to the input voltage and output current changes and the parameter perturbations. We also provide the conditions for the robust stability assurance of the closed‐loop system.     

Optimal linear estimation for continuous stochastic systems with random observation delays

This paper is concerned with the linear minimum mean square error estimation for Itô‐type differential equation systems with random delays, where the delay process is modeled as a finite‐state Markov chain. By first introducing a set of equivalent delay‐free observations and then defining two reorganized Markov chains, the estimation problem of random delayed systems is reduced to the one of delay‐free Markov jump linear systems. The estimator is derived by using the innovation analysis method based on the Itô differential formula. And the analytical solution to this estimator is given in terms of two Riccati differential equations that are of finite dimensions. Conditions for existence, uniqueness, and stability of the steady‐state optimal estimator are studied for time‐invariant cases. In this case, the obtained estimator is very easy to implement, and all calculation can be performed off line, leading to a linear time‐invariant estimator. Copyright © 2011 John Wiley & Sons, Ltd.     

Robust fusion time‐varying Kalman estimators for multisensor networked systems with mixed uncertainties

This paper addresses the problem of designing robust fusion time‐varying Kalman estimators for a class of multisensor networked systems with mixed uncertainties including multiplicative noises, missing measurements, packet dropouts, and uncertain‐variance linearly correlated measurement and process white noises. By the augmented approach, the original system is converted into a stochastic parameter system with uncertain noise variances. Furthermore, applying the fictitious noise approach, the original system is converted into one with constant parameters and uncertain noise variances. According to the minimax robust estimation principle, based on the worst‐case system with the conservative upper bounds of the noise variances, the five robust fusion time‐varying Kalman estimators (predictor, filter, and smoother) are presented by using a unified design approach that the robust filter and smoother are designed based on the robust Kalman predictor, which include three robust weighted state fusion estimators with matrix weights, diagonal matrix weights, and scalar weights, a modified robust covariance intersection fusion estimator, and robust centralized fusion estimator. Their robustness is proved by using a combination method, which consists of Lyapunov equation approach, augmented noise approach, and decomposition approach of nonnegative definite matrix, such that their actual estimation error variances are guaranteed to have the corresponding minimal upper bounds for all admissible uncertainties. The accuracy relations among the robust local and fused time‐varying Kalman estimators are proved. A simulation example is shown with application to the continuous stirred tank reactor system to show the effectiveness and correctness of the proposed results.     

Recursive methods for estimating the radial basis function‐based state‐dependent autoregressive model

Identifying a nonlinear radial basis function‐based state‐dependent autoregressive (RBF‐AR) time series model is the basis for solving the corresponding prediction and control problems. This paper studies some recursive parameter estimation algorithms for the RBF‐AR model. Considering the difficulty of the nonlinear optimal problem arising in estimating the RBF‐AR model, an overall forgetting gradient algorithm is deduced based on the negative gradient search. A numerical method with a forgetting factor is provided to solve the problem of determining the optimal convergence factor. In order to improve the parameter estimation accuracy, the multi‐innovation identification theory is applied to develop an overall multi‐innovation forgetting gradient (O‐MIFG) algorithm. The simulation results indicate that the estimation model based on the O‐MIFG algorithm can capture the dynamics of the RBF‐AR model very well.     

One Dimensional SDE Models, Low Order Numerical Methods and Simulation Based Estimation: A Comparison of Alternative Estimators

We evaluate the effects of several discretization schemes on alternative estimators of the drift parameters of stochastic differential equations, namely the continuous time MLE, a so-called naive estimator and an indirect estimator obtained through calibration. Two main results are evidenced: first, the importance of correctly generating data in a simulation based estimation procedure and second, the role of an indirect estimation procedure through calibration as a general strategy to be used every time the conditions of the estimation experiment are not the optimal ones.     

A Design Of Multiloop Predictive Self‐Tuning Pid Controllers

In this paper, a new design scheme of multiloop predictive self‐tuning PID controllers is proposed for multivariable systems. The proposed scheme firstly uses a static pre‐compensator as an approximately decoupling device, in order to roughly reduced the interaction terms of the controlled object. The static matrix pre‐compensator is adjusted by an on‐line estimator. Furthermore, by regarding the approximately decoupled system as a series of single‐input single‐output subsystems, a single‐input single‐output PID controller is designed for each subsystem. The PID parameters are calculated on‐line based on the relationship between the PID control and the generalized predictive control laws. The proposed scheme is numerically evaluated on a simulation example.     

Reduced‐order state estimation for linear time‐varying systems

We consider reduced‐order and subspace state estimators for linear discrete‐time systems with possibly time‐varying dynamics. The reduced‐order and subspace estimators are obtained using a finite‐horizon minimization approach, and thus do not require the solution of algebraic Lyapunov or Riccati equations. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Nonparametric kernel density estimation near the boundary

Standard fixed symmetric kernel-type density estimators are known to encounter problems for positive random variables with a large probability mass close to zero. It is shown that, in such settings, alternatives of asymmetric gamma kernel estimators are superior, but also differ in asymptotic and finite sample performance conditionally on the shape of the density near zero and the exact form of the chosen kernel. Therefore, a refined version of the gamma kernel with an additional tuning parameter adjusted according to the shape of the density close to the boundary is suggested. A data-driven method for the appropriate choice of the modified gamma kernel estimator is also provided. An extensive simulation study compares the performance of this refined estimator to those of standard gamma kernel estimates and standard boundary corrected and adjusted fixed kernels. It is found that the finite sample performance of the proposed new estimator is superior in all settings. Two empirical applications based on high-frequency stock trading volumes and realized volatility forecasts demonstrate the usefulness of the proposed methodology in practice.     

基于协方差配置的采样估计

在工程应用中,状态估计的指标要求常常表现为误差协方差的形式.在充分考虑系 统内采样特性的基础上,提出了采样估计协方差的定义和一种新的采样估计方法,目的在于 设计离散估计器使采样估计协方差达到指定值,从而获得满意的稳定状态估计性能.将此采 样估计问题等价地转化为一个虚拟离散系统的估计器设计问题,给出了期望估计器的存在条 件及显式表示.数值例子说明了方法的有效性.     

Robust, reduced-order, nonstrictly proper state estimation via the optimal projection equations with Petersen—Hollot bounds

A state-estimation design problem involving parametric plant uncertainties is considered. An error bound suggested by recent work of Petersen and Hollot is utilized for guaranteeing robust estimation. Necessary conditions which generalize the optimal projection equations for reduced-order state estimation are used to characterize the estimator which minimizes the error bound. The design equations thus effectively serve as sufficient conditions for synthesizing robust estimators. An additional feature is the presence of a static estimation gain in conjunction with the dynamic (Kalman) estimator, i. e., a nonstrictly proper estimator.     

Delay‐dependent fault estimation for uncertain time‐delay nonlinear systems: an LMI approach

This paper deals with the problem of robust fault estimation for uncertain time‐delay Takagi–Sugeno (TS) fuzzy models. The aim of this study is to design a delay‐dependent fault estimator ensuring a prescribed ??_∞ performance level for the fault estimation error, irrespective of the uncertainties and the time delays. Sufficient conditions for the existence of a robust fault estimator are given in terms of linear matrix inequalities (LMIs). Membership functions' (MFs) characteristics are incorporated into the fault estimator design to reduce the conservativeness of neglecting these characteristics. Finally, a numerical example is given to illustrate the effectiveness of the proposed design techniques. Copyright © 2006 John Wiley & Sons, Ltd.