A New Parameter Identification Algorithm for a Class of Second Order Nonlinear Systems: An On-line Closed-loop Approach

This paper presents a novel on-line closed-loop parameter identification algorithm for second order nonlinear systems. Parameter convergence of the proposed methodology is ensured by means of a rigorous Lyapunov-based analysis. The estimated parameters are obtained using the actual and an estimation system. Algebraic techniques are applied for estimating velocity and acceleration signals, which are required in the proposed algorithm. A comparative analysis allows assessing the performance of the new parameter identification algorithm with respect to on-line and off-line least squares algorithms. Numerical simulations indicate that the proposed methodology allows estimating different types of non-linearities, converges faster than other methodologies, is robust against disturbances, outperforms on-line techniques, and provides similar estimates as an off-line technique, but without requiring any type of data pre-processing.     

Adaptive parameter estimation for a general dynamical system with unknown states

This paper is concerned with the design of a state filter for a time‐delay state‐space system with unknown parameters from noisy observation information. The key is to investigate new identification algorithms for interactive state and parameter estimation of the considered system. Firstly, an observability canonical state‐space model is derived from the original model by linear transformation for the purpose of simplifying the model structure. Secondly, a direct state filter is formulated by minimizing the state estimation error covariance matrix on the basis of the Kalman filtering principle. Thirdly, once the unknown states are estimated, a state filter–based recursive least squares algorithm is proposed for parameter estimation using the least squares principle. Then, a state filter–based hierarchical least squares algorithm is derived by decomposing the original system into several subsystems for improving the computational efficiency. Finally, the numerical examples illustrate the effectiveness and robustness of the proposed algorithms.     

估计传递函数参数的误差校正法*

本文提出一种称为误差校正法的估计传递函数参数的方法,建立了目标函数与传递函数参数及其最小二乘估值偏差间的函数关系,在完成最小二乘估计的基础上,通过连续修正,使传递函数估值精度得到提高,算例表明,该法比普通最小二乘法和广义最小二乘法的精度高,而且,比广义最小二乘法收敛得快。     

Hierarchical Newton and least squares iterative estimation algorithm for dynamic systems by transfer functions based on the impulse responses

This paper develops a parameter estimation algorithm for linear continuous-time systems based on the hierarchical principle and the parameter decomposition strategy. Although the linear continuous-time system is a linear system, its output response is a highly nonlinear function with respect to the system parameters. In order to propose a direct estimation algorithm, a criterion function is constructed between the response output and the observation output by means of the discrete sampled data. Then a scheme by combining the Newton iteration and the least squares iteration is builded to minimise the criterion function and derive the parameter estimation algorithm. In light of the different features between the system parameters and the output function, two sub-algorithms are derived by using the parameter decomposition. In order to remove the associate terms between the two sub-algorithms, a Newton and least squares iterative algorithm is deduced to identify system parameters. Compared with the Newton iterative estimation algorithm without the parameter decomposition, the complexity of the hierarchical Newton and least squares iterative estimation algorithm is reduced because the dimension of the Hessian matrix is lessened after the parameter decomposition. The experimental results show that the proposed algorithm has good performance.     

Efficient algorithm for a class of least squares estimationproblems

A computationally efficient algorithm for solving least squares estimation problems is proposed. It is well suited for problems with the normal equation matrix factorizable in terms of Kronecker's products. Three classes of identification problems factorizable in this sense are pointed out. Computational complexity of the algorithm and its robustness against round off errors is also discussed     

Data filtering based least squares iterative algorithm for parameter identification of output error autoregressive systems

This letter derives a data filtering based least squares iterative identification algorithm for output error autoregressive systems. The basic idea is to use the data filtering technique to transform the original identification model to an equation error model and to estimate the parameters of this model. The proposed algorithm is more efficient and can produce more accurate parameter estimation than the existing least squares iterative algorithm.     

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.     

Optimal Quantization of Signals for System Identification

In this technical note, we examine the optimal quantization of signals for system identification. We deal with memoryless quantization for the output signals and derive the optimal quantization schemes. The objective functions are the errors of least squares parameter estimation subject to a constraint on the number of subsections of the quantized signals or the expectation of the optimal code length for either high or low resolution. The optimal quantizer has the property that it is coarse near the origin of its output and becomes dense away from the origin in the usual situation. Finally the required quantity of data to decrease the total parameter estimation error, caused by quantization and noise, is discussed.      

基于准最小二乘法的光伏阵列模型鲁棒参数估计方法

光伏阵列的模型参数估计在光伏发电系统的仿真、输出功率预测、最大功率点跟踪等方面有重要意义。当测量数据中只含随机误差时,以加权最小二乘（WLS）为优化函数的参数估计方法有较好的辩识效果。但是当测量数据中含有显著误差时,WLS参数辩识的效果较差。为解决此问题,本文提出了一种以准加权最小二乘法（QWLS）为优化函数的参数估计方法来减小显著误差的影响,采用了赤池信息量准则(AIC)设计QWLS最优参数,将该方法应用于光伏阵列中构造模型鲁棒参数估计问题。最后将WLS和QWLS分别结合序列二次规划（SQP）算法,进行光伏阵列模型的参数估计仿真与实验测试。测试结果显示QWLS参数估计结果更准确,验证了准最小二乘法的鲁棒性与有效性。     

有色噪声干扰下Hammerstein非线性系统两阶段辨识

针对实际工业过程中普遍存在有色噪声,提出了有色噪声干扰下Hammerstein非线性系统两阶段辨识方法。采用设计的组合式信号实现Hammerstein系统各模块参数辨识分离,简化了辨识过程。在第一阶段,基于可分离信号的输入输出数据,利用相关分析算法估计线性模块参数,减少了有色噪声对辨识的干扰。在第二阶段,基于随机信号的...     

A cumulant based algorithm for the identification of input-output quadratic systems

The identification of a special class of polynomial models is pursued in this paper. In particular a parameter estimation algorithm is developed for the identification of an input-output quadratic model excited by a zero mean white Gaussian input and with the output corrupted by additive measurement noise. Input-output crosscumulants up to the fifth order are employed and the identification problem of the unknown model parameters is reduced to the solution of successive triangular linear systems of equations that are solved at each step of the algorithm. Simulation studies are carried out and the proposed methodology is compared with two least squares type identification algorithms, the output error method and a combination of the instrumental variables and the output error approach. The proposed cumulant based algorithm and the output error method are tested with real data produced by a robotic manipulator.     

Adaptive Control Scheme for Large‐Scale Interconnected Systems Described by Hammerstein Models

This paper proposes an adaptive algorithm for the online control of discrete‐time large‐scale nonlinear systems, which reduces the noise effects acting on the system output (regulation problem) and allows the system output to keep track of a time‐varying trajectory (tracking problem). We consider a large‐scale nonlinear system that can be decomposed into single‐input single‐output (SISO) interconnected nonlinear subsystems with known structure variables (orders, delays) and unknown time‐varying parameters. Each interconnected subsystem is described by block‐oriented models, specifically a discrete‐time Hammerstein model. Parameter adaptation is performed using a recursive parametric estimation algorithm based on the adjustable model method and the least squares techniques. Simulation results of an interconnected petroleum process are provided to demonstrate the effectiveness of the developed control scheme.     

An iterative Kalman smoother/least-squares algorithm for the identification of delta-ARX models

Additive measurement noise on the output signal is a significant problem in the δ-domain and disrupts parameter estimation of auto-regressive exogenous (ARX) models. This article deals with the identification of δ-domain linear time-invariant models of ARX structure (i.e. driven by known input signals and additive process noise) by using an iterative identification scheme, where the output is also corrupted by additive measurement noise. The identification proceeds by mapping the ARX model into a canonical state-space framework, where the states are the measurement noise-free values of the underlying variables. A consequence of this mapping is that the original parameter estimation task becomes one of both a state and parameter estimation problem. The algorithm steps between state estimation using a Kalman smoother and parameter estimation using least squares. This approach is advantageous as it avoids directly differencing the noise-corrupted ‘raw’ signals for use in the estimation phase and uses different techniques to the common parametric low-pass filters in the literature. Results of the algorithm applied to a simulation test problem as well as a real-world problem are given, and show that the algorithm converges quite rapidly and with accurate results.     

Adaptive stiffness estimation for compliant robotic manipulation using stochastic disturbance models

To achieve haptic telepresence and proper contact behaviour, the control action of a robotic manipulator must be designed with respect to contact parameters. Unfortunately, it is hard to know these parameters exactly in unknown or partly known environments. In this case, contact instability and poor dynamic accuracy can arise due to the presence of modelling errors in the control design. To overcome these problems, online estimation of the relevant contact parameters can be performed, with corresponding adaptation of control laws. This article presents an algorithm for online stiffness estimation for compliant robotic manipulation based on the extended state-space representation of the system and force signals. No position or velocity measurements are required. The algorithm, supported by theoretical analysis, uses offline data concerning several stiffness mismatch scenarios and, through a least square error analysis, computes an estimate of the stiffness value. Simulation results are presented, with fast and accurate estimation even in the presence of noise, highlighting the merits of the method.     

面向应用的RGB-D机器人道路坡度融合估计方法

为提高机器人在移动路径中对道路坡度的估计精度,提出一种面向应用的RGB-D(red green blue-depth)机器人融合型道路坡度估计方法。首先,引入随机采样一致性算法完成点云处理;其次,采用改进型平面拟合方法完成法向量估计;最后,采用余弦聚类及累加平均方法实现高精度道路坡度估计。实验结果表明,该算法在数据集下相较最小二乘法与稀疏子空间法,估计误差分别降低1.21%、2.13%,在实际环境下较最小二乘法平均误差降低1.43°,这证明了所提方法的可行性和准确性。     

A novel robust position estimator for self-sensing magnetic levitation systems based on least squares identification

In this work a novel method is introduced for the estimation of the position of a self-sensing magnetic levitation system, based on a least squares identification strategy. In the first step, a detailed mathematical model of the magnetic levitation system is derived and the properties of this system are analyzed for the case of a pulse-width modulated control. Based on this model, an estimation algorithm for the inductance of the magnetic levitation system is introduced. In classical position estimation schemes known form the literature large estimation errors are typically induced by a deviation of the electric resistance from its nominal value or by a fast motion of the levitated object. In this work it is shown that these errors can be exactly compensated by means of a suitable estimation strategy. Furthermore, it is outlined that the chosen structure of the estimation scheme allows for a very efficient implementation in real-time hardware. Afterwards, the design of a cascaded position controller for the magnetic levitation system is briefly summarized. Finally, the excellent quality and the high robustness of the proposed position estimator is demonstrated by means of simulation studies and measurement results on a test bench.     

衰减激励条件下递阶最小二乘辨识的均方收敛性

为减少递推辨识的计算量，提出了递阶辨识原理，它是将系统分解为多个维数较小的虚拟子系统进行辨识，从而获得递阶最小二乘辨识方法。在衰减激励条件下，针对时不变系统研究了递阶最小二乘法的收敛性，得到了参数估计误差均方收敛于零时衰减指数应满足的条件。递阶最小二乘具有良好的性能，其计算量比递推量小二乘辨识要小得多，并具有容易实现等优点。     

Indirect adaptive robust control of nonlinear systems with time‐varying parameters in a strict feedback form

Without any prior knowledge of the physical bounds of unknown parameters and uncertain nonlinearities, an indirect adaptive robust controller is constructed for uncertain nonlinear time‐varying systems in a strict‐feedback form. Firstly, an adaptive strong robust controller is derived based on the command filtered adaptive backstepping approach. This controller not only can guarantee the boundedness of the closed‐loop system signals in the presence of time‐varying (TV) parameters and uncertain nonlinearities but also obviate the need to compute analytic derivatives of virtual control functions. Thus, the problem of “explosion of terms” in the standard adaptive backstepping technique is avoided. Through introduction of a simple adaptation law on the upper bound of uncertainties, a smooth robust control term is used to realize the disturbance attenuation. Afterwards, based on the nonlinear X‐swapping techniques, a modular approach in which the controller and the identifier can be designed separately is exploited. A novel algorithm is proposed to estimate the TV parameters accurately. By adopting the variation trend of the covariance matrix as an indicator of the driving signals' persistent excitation level, this online parameter estimation law is switched between a modified least‐squares algorithm and a gradient algorithm based on fixed σ‐modification. Finally, a series of properties on the asymptotic stability and the global uniform ultimate boundedness of the closed‐loop system is established. Simulation results verify the effectiveness of the suggested method.     

时变系统辨识的多新息方法

推广了估计时不变参数的单新息修正技术,提出了多新息辨识方法.该方法可以抑制坏数据对参数估计的影响,具有较强的鲁棒性.分析表明多新息方法可以跟踪时变参数,计算量也较遗忘因子最小二乘法和卡尔曼(Kalman)滤波算法要小.仿真结果说明多新息算法估计系统参数是有效的.