Robust discrete‐time output feedback model reference control design with state and unknown input estimation

For MIMO discrete‐time linear systems with unknown input in which the matching condition does not hold, the use of estimation method in an output feedback controller is proposed in this paper. Provided that the variation of unknown input in the two consecutive sampling instances is not changed significantly, both the system state and unknown input can be simultaneously estimated by our proposed observer algorithm with the estimation error being constrained in a small bounded region of the order of O(T). Then, a method utilizing command generator tracker is designed to generate the reference model. Concurrently with the estimations of the system state and unknown input are used in the controller where it can cause the tracking error to be bounded in a small region with the guaranteed system stability. Finally, the feasibility of our algorithm can be proved to be valid through the demonstration of a simulation‐based example. Copyright © 2008 John Wiley & Sons, Ltd.     

一种约束输入输出的隐式广义预测控制新算法

基于CARIMA模型提出了一种约束输入输出的隐式广义预测控制算法.针对广义预测控制问题,在整个预测时域和控制时域,对输入幅值,输入增量和输出幅值施加了约束,引入了输入输出柔化系数,从而简化了目标函数,减小了计算量,该算法不必求解逆矩阵;并采用了隐式广义预测自校正控制算法,利用并列预测控制器间的特点,直接辨识输出预测器中的参数,从而避免了在线求解Diophantine方程.该算法占用内存小,计算速度快,仿真结果表明该算法具有良好的控制性能.     

DISCRETE‐TIME OBSERVER‐BASED OUTPUT TRACKING CONTROLLER DESIGN FOR NONMINIMUM PHASE SYSTEMS WITH PERTURBATIONS

In this paper, an observer‐based output tracking controller for an SISO nonminimum phase discrete‐time system is proposed. When the disturbances between two consecutive sampling instances do not vary significantly, the observer algorithm can simultaneously estimate the system states and the unknown perturbation, and can render the estimation errors of system states and perturbation constrained in a small bounded region. The control law, including a feedforward term and a feedback input, can make the tracking error constrained in a small bounded region with guaranteed system stability. A numerical example is presented to demonstrate the applicability of the proposed control scheme.     

Kalman filter based estimation algorithm for the characterization of the spatiotemporal hemodynamic response in the brain

The characterization of the spatiotemporal hemodynamic response (stHR) in the brain is important for understanding the interaction between neighboring brain voxels and regions. In this paper, we design an identification algorithm for the characterization of the cerebral stHR which is modeled by a system of coupled hyperbolic partial differential equation (PDE) and infinite-dimensional ordinary differential equation (ODE). The proposed algorithm provides estimates of the hemodynamic variables (cerebral blood flow and mass density contributed by blood) and physiological parameters using non-invasive Blood Oxygenation Level Dependent (BOLD) data measured with functional Magnetic Resonance Imaging (fMRI) modality. The proposed solution concept follows three main steps: (i) discretization of the stHR model using Galerkin-based finite element method; (ii) estimation of the output derivative using high-order sliding mode differentiator; and (iii) estimation of the state, input, and parameters from sampled-in-space measurements using the reduced-order approximation model and a constrained extended Kalman filter with unknown input algorithm. In addition, sufficient conditions that depend on the chosen discretization scheme, and which guarantee the structural identifiability of the input and parameters, and also the observability of the system are provided. The performance of the proposed algorithm is assessed using both synthetic and real data. The set of the used real data represents the 1-D BOLD signal collected from the visual cortex and acquired in 3 Tesla fMRI scanner.     

An optimal IV technique for identifying continuous-time transfer function model of multiple input systems

An instrumental variable method for continuous-time model identification is proposed for multiple input single output systems where the characteristic polynomials of the transfer functions associated with each input are not constrained to be identical. An associated model order determination procedure is shown to be reasonably successful. Monte Carlo simulation analyses are used to demonstrate the properties and general robustness of the model order selection and parameter estimation schemes. The results obtained to model a winding process and an industrial binary distillation column illustrate the practical applicability of the proposed identification scheme.     

Optimal experiment design for linear systems with input-output constraints

The problem of optimal experiment design for parameter estimation in linear dynamic systems is studied. Results relating to both constrained input and output variances are established. For the case of constrained input variance, it is shown that a D-optimal experiment exists in which the system input is generated externally provided the system and noise transfer functions have no common parameters. For the case of constrained output variance, it is shown that an experiment in which the system input is generated by a combination of a minimum variance control law together with an external set point perturbation is D-optimal for certain classes of systems. Other related results are also presented which illustrate the role of feedback in optimal experiment design.     

Multirate constrained adaptive control

An adaptive servo control law with input constraints is derived for application to linear time-invariant systems with unknown parameters and two sampling rates: a slower one for the output, and a faster one for the input. The error between the actual and a reference performance index is shown to be bounded by the product of a finite gain and the parameter estimation error in the limit sense. Sufficient conditions for parameter convergence are proven under which the performance of the multirate, adaptive constrained control system asymptotically approaches that of the analogous single (fast) rate, constrained control system with known, constant parameters. The advantages of the multirate, adaptive constrained control algorithm are demonstrated by numerical simulations.     

Autoregressive models in stochastic approximation algorithms for parameter estimation

This paper describes an on-line procedure for estimating the parameters of linear discrete time systems when input and output are subjected to measurement noise of unknown statistics. The algorithm is derived through stochastic approximation, To ensure unbiased parameter estimates, the correlated part of the residuals are first estimated by modelling the residuals as an autoregressive series, and then subtracted from the estimated residuals. The algorithm estimates the system parameters and noise parameters simultaneously. Three gain expressions are derived for the estimation algorithm. They are («) scalar gain, (b) diagonal matrix gain, and (c) square matrix gain.     

Combining state estimator and disturbance observer in discrete‐time sliding mode controller design

In response to a multiple input/multiple output discrete‐time linear system with mismatched disturbances, an algorithm capable of performing estimated system states and unknown disturbances is proposed first, and then followed with the design of the controller. Attributed to the fact that both system states and disturbances can be estimated simultaneously with our proposed method, the estimation error is constrained at less than O(T) as the disturbance between the two sampling points is insignificant. In addition, the estimated system states and disturbances are then to be used in the controller when implementing our algorithm in a non‐minimum phase system (with respect to the relation between the output and the disturbance). The tracking error is constrained in a small bounded region and the system stability is guaranteed. Finally, a numerical example is presented to demonstrate the applicability of the proposed control scheme. Copyright © 2008 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Adaptive model predictive control for a class of constrained linear systems based on the comparison model

This paper proposes an adaptive model predictive control (MPC) algorithm for a class of constrained linear systems, which estimates system parameters on-line and produces the control input satisfying input/state constraints for possible parameter estimation errors. The key idea is to combine the robust MPC method based on the comparison model with an adaptive parameter estimation method suitable for MPC. To this end, first, a new parameter update method based on the moving horizon estimation is proposed, which allows to predict an estimation error bound over the prediction horizon. Second, an adaptive MPC algorithm is developed by combining the on-line parameter estimation with an MPC method based on the comparison model, suitably modified to cope with the time-varying case. This method guarantees feasibility and stability of the closed-loop system in the presence of state/input constraints. A numerical example is given to demonstrate its effectiveness.     

基于循环平稳二阶统计量的SUB-CMOE盲均衡算法

提出了一种新的利用循环二阶统计量估计信道的盲均衡算法.通过对信道输出信号进行过采样,建立单输入多输出(single input multiple output,SIMO)信道模型.传统的约束最小输出能量算法(constrained minimum output energy algorithm,CMOE)只研究了理想的无噪声状态,不考虑噪声对信道的影响.然而实际中噪声是不可避免的.为了使得约束最小能量算法可以适用于有噪声环境,利用子空间算法来消除噪声对算法的影响.仿真结果表明本算法可以克服噪声对信道的影响,收敛速度快.     

Simultaneous pole-placement/stabilization of pairs of linear time-invariant plants using a continuous-time periodic controller

Given a pair of single input single output (SISO), linear time-invariant (LTI), and strictly proper plants of relative order r, this paper employs a continuous-time periodic controller to achieve 1) simultaneous pole-placement for r = 1 and 2) guaranteed simultaneous stabilization for r = 2; 3, and 4, which jobs LTI controllers cannot, in general, do. The controller also ensures insignificant output ripples. The analysis is based on averaging principle. The computational steps for controller synthesis are linear algebraic in nature. An example illustrates the design procedure.     

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.     

UD分解与偏差补偿结合用于变量带误差模型辨识

本文提出一种基于UD(upper-diagonal)分解与偏差补偿结合的辨识方法,用于变量带误差(errors-in-variables,EIV)模型辨识.考虑单输入单输出(single input and single output,SISO)线性动态系统,当输入和输出含有零均值、方差未知的高斯测量白噪声时,该类系统的模型参数估计是一种典型的EIV模型辨识问题.为了获得这种EIV模型参数的无偏估计,本文先推导出最小二乘模型参数估计偏差量与输入输出噪声方差以及最小二乘损失函数与输入输出噪声方差的关系,然后采用UD分解方法递推获得模型参数估计值,再利用输入输出噪声方差估计值补偿模型参数估计偏差,以此获得模型参数的无偏估计.本文还讨论了算法实现过程中遇到的一些问题及修补方法,并通过仿真例验证了所提辨识方法的有效性.     

基于带有噪声输入的稀疏高斯过程的人体姿态估计

高斯过程回归（Gaussian process regression，GPR）是一种广泛应用的回归方法，可以用于解决输入输出均为多元变量的人体姿态估计问题.计算复杂度是高斯过程回归的一个重要考虑因素，而常用的降低计算复杂度的方法为稀疏表示算法.在稀疏算法中，完全独立训练条件（Fully independent training conditional，FITC）法是一种较为先进的算法，多用于解决输入变量彼此之间完全独立的回归问题.另外，输入变量的噪声问题是高斯过程回归的另一个需要考虑的重要因素.对于测试的输入变量噪声，可以通过矩匹配的方法进行解决，而训练输入样本的噪声则可通过将其转换为输出噪声的方法进行解决，从而得到更高的计算精度.本文基于以上算法，提出一种基于噪声输入的稀疏高斯算法，同时将其应用于解决人体姿态估计问题.本文实验中的数据集来源于之前的众多研究人员，其输入为从视频序列中截取的图像或通过特征提取得到的图像信息，输出为三维的人体姿态.与其他算法相比，本文的算法在准确性，运行时间与算法稳定性方面均达到了令人满意的效果.     

参数估计的Systolic算法

本文根据最小二乘原理在三角形Ｓｙｓｔｏｌｉｃ阵列上实现了单输入单输出系统的递推参数估计算法，首先利用矩阵的三角分解给出了待估参数及协方差阵的递推公式，然后利用正交平面旋转并结合三角形Ｓｙｓｔｏｌｉｃ阵列的特点给出了相应的Ｓｙｓｔｏｌｉｃ递推参数估计算法，最后还考虑了算法实现时的性能指标，其后是一些数值仿真结果，由于文中利用了正交平面旋转，因而所得算法是数值稳定的。     

Parameter estimation of stochastic linear systems with noisy input

This paper addresses the problem of parameter estimation of stochastic liner systems with noisy input–output measurements. A new and simple estimation scheme for the variances of the white input and output measurement noises is presented, which is only based on expanding the denominator polynomial of the system transfer function and makes no use of the average least-squares errors. The attractive feature of the iterative least-square based parametric algorithm thus developed is its improved convergence property. The effectiveness of the developed identification algorithm is demonstrated through numerical illustrations.     

Time delay estimation for MIMO dynamical systems – With time-frequency domain analysis

In MIMO dynamical systems, the time delay estimation (TDE) problem between each output and input is often confounded due to the dynamic interaction between the inputs and the outputs. In this paper, analyses are given in the time, frequency and time-frequency domains, from which a novel TDE method using combined continuous wavelet transform (CWT) and cross correlation is conceived. In the proposed method, a series of time delays over scales (frequencies) are calculated and an unbiased estimation is deduced from them, by calculating and handling the cross correlation between the CWT coefficients of system input and output data. The TDE method in closed loop case is also studied. Numerical examples with simulation and experimental data verify the feasibility and effectiveness of the proposed method.     

延时双线性系统参数估计的一种新方法——Fourier级数法

本文提出了一种用Fourler级数来估计延时双线性系统模型参数的新方法.通过Fourier 级数的延时分析法,把原延时双线性系统方程转换成可用输入输出信息来确定待定参数的代 数方程,最后用最小二乘法得到参数的估计值.与Walsh级数方法相比本文给出的运算矩阵 精确度更高,并且在输入信息是正弦信号时,计算过程相当简洁.     

Kalman filter-based identification for systems with randomly missing measurements in a network environment

We consider the problem of parameter estimation and output estimation for systems in a transmission control protocol (TCP) based network environment. As a result of networked-induced time delays and packet loss, the input and output data are inevitably subject to randomly missing data. Based on the available incomplete data, we first model the input and output missing data as two separate Bernoulli processes characterised by probabilities of missing data, then a missing output estimator is designed, and finally we develop a recursive algorithm for parameter estimation by modifying the Kalman filter-based algorithm. Under the stochastic framework, convergence properties of both the parameter estimation and output estimation are established. Simulation results illustrate the effectiveness of the proposed algorithms.