非线性参数估计中最优解的一个充分条件

估一类非线性参数估计问题中，当某个容许参的输出值与给定值的误差范数为局部极小时，如何判断这个参数是最优解。     

Adaptive linear finite-element method for modelling nonlinear dynamic systems

This paper proposes a method of identifying nonlinear dynamic models with observation data (or a training data set) which exhibits a simple structure, adaptive input-space partition and fast convergence. The method employs the multiscale approximation concepts which have been introduced in numerical analysis motivated by wavelet analysis concepts. The partition or equivalently scaled basis functions are determined and selected adaptively in a sequenced and ordered manner. This method may be also considered as a single-layer neural network but with adaptive neural neurons. The number of multiscale basis functions required depends on the degree of nonlinearity of the system being modelled. The method is compared with the cerebellar model with interpolation (CEINT) and the cerebellar model articulation control (CMAC) methods and has been shown to achieve comparative modelling accuracies but with a reduced memory space and a concomitantly reduced training set.     

Multi-output parameter estimation of dynamic systems by output shapes

A multi-output method of parameter estimation is introduced for dynamic systems that relies on the shape attributes of model outputs. The shapes of outputs in this method are represented by the surfaces that are generated by continuous wavelet transforms (CWTs) of the outputs in the time-scale domain. Since the CWTs also enhance the delineation of outputs and their sensitivities to model parameters in the time-scale domain, regions in the time-scale plane can be identified wherein the sensitivity of the output with respect to one model parameter dominates all the others. This allows approximation of the prediction error in terms of individual model parameters in isolated regions of the time-scale domain, thus enabling parameter estimation based on a small set of wavelet coefficients. These isolated regions of the time-scale plane also reveal numerous transparencies to be exploited for parameter estimation. It is shown that by taking advantage of these transparencies, the robustness of parameter estimation can be improved. The results also indicate the potential for improved precision and faster convergence of the parameter estimates when shape attributes are used in place of the magnitude.     

Identifiability of errors in variables dynamic systems

There has been substantial research carried out on the errors in variables (EIV) identifiability problem for dynamic systems. These results are spread across a significant volume of literature. Here, we present a single theorem which compactly summarizes many of the known results. The theorem also covers several cases which we believe to be novel. We analyze single input single output systems using second order properties. We also extend the results to a class of multivariable systems.     

Parameter identification for models with bounded errors in all variables

In this paper, the problem of parameter identification for models with bounded measurement errors both on the input and on the output is addressed and some corrections to previously published results are presented. In particular, it is shown that only parameter overbounds can in general be computed for systems of the form y = (φ + δφ)θ + δy when the bounded measurement errors δφ and δy are correlated. Since ARMAX and bilinear systems can be represented in this form, it turns out that tight parameter bounds are in general not available for these systems. Finally, we show that it is possible to check a posteriori whether the obtained bounds are tight or not.     

A method for parameter estimation of a class of non-linear distributed systems under noisy observations

A method is presented for estimating an unknown parameter of a distributed parameter system which depends on the system state. The system considered is modelled by a class of non-linear partial differential equations of a parabolic type. Noisy observations are assumed to be taken through an arbitrary number of sensors allocated on the spatial region. First, the explicit form of the stationary solution of the state equation is discussed. Second, use is made of the maximum likelihood approach to obtain the optimal estimate of the unknown parameter. Consistency properties w.p.1 of the optimal estimate obtained are also shown. Finally, results of digital simulation experiments are included to support the theoretical aspects.     

Performance analysis of the auxiliary model-based least-squares identification algorithm for one-step state-delay systems

Based on the input–output representation of one-step state-delay systems, we use the auxiliary model-based recursive least-squares algorithm to estimate the parameters of the systems and study the convergence of the proposed algorithm by using the stochastic process theory. A simulation example is provided.     

Optimal state estimation for networked systems with random parameter matrices,correlated noises and delayed measurements

In this paper, the optimal least-squares state estimation problem is addressed for a class of discrete-time multisensor linear stochastic systems with state transition and measurement random parameter matrices and correlated noises. It is assumed that at any sampling time, as a consequence of possible failures during the transmission process, one-step delays with different delay characteristics may occur randomly in the received measurements. The random delay phenomenon is modelled by using a different sequence of Bernoulli random variables in each sensor. The process noise and all the sensor measurement noises are one-step autocorrelated and different sensor noises are one-step cross-correlated. Also, the process noise and each sensor measurement noise are two-step cross-correlated. Based on the proposed model and using an innovation approach, the optimal linear filter is designed by a recursive algorithm which is very simple computationally and suitable for online applications. A numerical simulation is exploited to illustrate the feasibility of the proposed filtering algorithm.     

Adaptive control for output feedback nonlinear systems in the presence of modeling errors

The paper is extending output feedback nonlinear control and backstepping approaches to a class of systems approximately diffeomorphic to output feedback systems that include unknown functions. The unknown functions are addressed via online function approximation, which results in two types of uncertainty. Parametric uncertainty due to online function approximation and non-parametric uncertainty. The non-parametric uncertainty results from the inability of any function approximator to perfectly model an unknown function and from terms unmodeled by the output feedback form. The non-parametric terms are assumed to be bounded by unknown constants. The backstepping procedure is applied to adapt with respect to both parametric uncertainties and the upper bound on the non-parametric uncertainties.     

A sparse direction-of-arrival estimation algorithm for MIMO radar in the presence of gain-phase errors

In this paper, the problem of direction-of-arrival (DOA) estimation for monostatic multiple-input multiple-output (MIMO) radar with gain-phase errors is addressed, by using a sparse DOA estimation algorithm with fourth-order cumulants (FOC) based error matrix estimation. Useful cumulants are designed and extracted to estimate the gain and the phase errors in the transmit array and the receive array, thus a reliable error matrix is obtained. Then the proposed algorithm reduces the gain-phase error matrix to a low dimensional one. Finally, with the updated gain-phase error matrix, the FOC-based reweighted sparse representation framework is introduced to achieve accurate DOA estimation. Thanks to the fourth-order cumulants based gain-phase error matrix estimation, and the reweighted sparse representation framework, the proposed algorithm performs well for both white and colored Gaussian noises, and provides higher angular resolution and better angle estimation performance than reduced-dimension MUSIC (RD-MUSIC), adaptive sparse representation (adaptive-SR) and ESPRIT-based algorithms. Simulation results verify the effectiveness and advantages of the proposed method.     

Optimum parameter for the SOR-like method for augmented systems

Recently, several proposals for the generalization of Young's SOR method to the saddle point problem or the augmented system has been presented. One of the most practical versions is the SOR-like method given by Golub et al., [(2001). SOR-like methods for augmented systems. BIT, 41, 71–85.], where the convergence and the determination of its optimum parameters were given. In this article, a full characterization of the spectral radius of the SOR-like iteration matrix is given, and an explicit expression for the optimum parameter is given in each case. The new results also lead to different results to that of Golub et al. Besides, it is shown that by the choices of the preconditioning matrix, the optimum SOR-like iteration matrix has no complex eigenvalues, therefore, it can be accelerated by semi-iterative methods.     

Identification of stochastic linear systems in presence of input noise

Most identification methods rely on the assumption that the input is known exactly. However, when collecting data under an identification experiment it may not be possible to avoid noise when measuring the input signal. In the paper some different ways to identify systems from noisy data are discussed. Sufficient conditions for identifiability are given. Also accuracy properties and the computational requirements are discussed. A promising approach is to treat the measured input and output signals as outputs of a multivariable stochastic system. If a prediction error method is applied using this approach the system will be identifiable under mild conditions.     

Extended Kalman filters for fractional‐order nonlinear continuous‐time systems containing unknown parameters with correlated colored noises

By using the Grünwald‐Letnikov (G‐L) difference method and the Tustin generating function method, this study presents extended Kalman filters to achieve satisfactory state estimation for fractional‐order nonlinear continuous‐time systems that containing some unknown parameters with the correlated fractional‐order colored noises. Based on the G‐L difference method and the Tustin generating function method, the difference equations corresponding to fractional‐order nonlinear continuous‐time systems are constructed respectively. The first‐order Taylor expansion is used to linearize the nonlinear functions in the estimated system, which provides the system model for extended Kalman filters. Using the augmented vector method, the unknown parameters are regarded as new state vectors, and the augmented difference equation is constructed. Based on the augmented difference equation, extended Kalman filters are designed to estimate the state of fractional‐order nonlinear systems with process noise as fractional‐order colored noise or measurement noise as fractional‐order colored noise. Meanwhile, the extended Kalman filters proposed in this paper can also estimate the unknown parameters effectively. Finally, the effectiveness of the proposed extended Kalman filters is validated in simulation with two examples.     

含未知参数的一维人群动态系统的自适应边界控制

针对一类存在扰动的一维人群动态系统,在扩散系数及边界条件系数未知的情况下,设计自适应边界控制律来控制人群向设定的方向平稳疏散.借助李雅普诺夫稳态判据对自适应边界控制律作用下的人群动态系统的稳定性给出了详细的证明.系统的建模及稳定性的证明均在分布参数系统的范畴内完成,避免了模型降阶方法引起的误差的产生.通过一个仿真实例,对比人群动态系统在未施加外部控制, Robin边界控制及自适应边界控制三种情况下,当扩散系数取不同数值时,人群密度的演化情况,验证了自适应边界控制律的有效性.     

Comparison of experimental designs for simulation-based symbolic regression of manufacturing systems

In this article, an empirical analysis of experimental design approaches in simulation-based metamodelling of manufacturing systems with genetic programming (GP) is presented. An advantage of using GP is that prior assumptions on the structure of the metamodels are not required. On the other hand, having an unknown structure necessitates an analysis of the experimental design techniques used to sample the problem domain and capture its characteristics. Therefore, the study presents an empirical analysis of experimental design methods while developing GP metamodels to predict throughput rates in a common industrial system, serial production lines. The objective is to identify a robust sampling approach suitable for GP in simulation-based metamodelling. Experiments on different sizes of production lines are presented to demonstrate the effects of the experimental designs on the complexity and quality of approximations as well as their variance. The analysis showed that GP delivered system-wide metamodels with good predictive characteristics even with the limited sample data.     

Consistency of the extended gradient identification algorithm for multi-input multi-output systems with moving average noises

The consistency of identification algorithms for systems with colored noises is a main topic in system identification. This paper focuses on the extended stochastic gradient (ESG) identification algorithm for the multivariable linear systems with moving average noises. By integrating the noise regression terms and the noise model parameters into the information matrix and the parameter vector, and based on the gradient search principle, the ESG algorithm is presented. The unknown noise terms in the information matrix are replaced with their estimates. The convergence analysis shows that the parameter estimation error converges to zero under a persistent excitation condition. Two simulation examples are given to illustrate the effectiveness of the algorithm.     

具有分片非线性输入的Wiener系统的随机梯度迭代(英文)

研究了一类具有分片非线性输入(又称为死区非线性输入)的Wiener系统的参数辨识,分片非线性输入是一个强非线性输入,其数学模型不能写成参数乘以输入的形式,首先引入开关函数,接着利用开关函数将原系统的不可辨识模型转换为可辨识模型,然后通过随机梯度迭代方法辨识出系统的参数,利用辨识出的参数可以计算出系统所有待辨识参数。仿真结果证明了本文方法的有效性。     

Finite-time estimation for a class of systems with unknown time-delay using modulating functions-based method

Time-delay systems are widely used to model real problems. Most of the works on such systems assume prior knowledge of the delay, which is mostly unknown in real applications. This paper aims to fast and robustly estimate unknown delay, parameters, and output derivatives for a class of linear time-delay systems in noisy environment. First, the classical modulating functions method is combined with the recursive least square algorithm and the Gauss–Newton method to estimate the coefficients and the time-delay, respectively. Second, the generalized modulating functions method is adopted to provide algebraic integral formulas to estimate the output derivatives using the estimated parameters. Finally, numerical simulations are given to demonstrate the efficiency and robustness of the proposed methods.     

Auxiliary model multiinnovation stochastic gradient parameter estimation methods for nonlinear sandwich systems

This article studies the identification problem of the nonlinear sandwich systems. For the sandwich system, because there are inner variables which cannot be measured in the information vector of the identification models, it is difficult to identify the nonlinear sandwich systems. In order to overcome the difficulty, an auxiliary model is built to predict the estimates of inner variables by means of the output of the auxiliary model. For the purpose of employing the real‐time observed data, a cost function with dynamical data is constructed to capture on‐line information of the nonlinear sandwich system. On this basis, an auxiliary model stochastic gradient identification approach is proposed based on the gradient optimization. Moreover, an auxiliary model multiinnovation stochastic gradient estimation method is developed, which tends to enhance estimation accuracy by introducing more observed data dynamically. The numerical simulation is provided and the simulation results show that the proposed auxiliary model identification method is effective for the nonlinear sandwich systems.     

State estimation for nonlinear systems under model uncertainties: a class of sliding-mode observers

This paper deals with the classical problem of state estimation, considering partially unknown, nonlinear systems with noise measurements. Estimation of both, state variables and unstructured uncertain term, are performed simultaneously. In order to transform the measured disturbance into system disturbance, an alternative system representation is proposed, which lead a more advantageous observer structure. The observer proposed contains a proportional-type contribution and a sliding term for the measurement of error, which provides robustness against noisy measurements and model uncertainties. Convergence analysis of the estimation methodology proposed is performed, analysing the equation of the dynamics of the estimation error; it is shown that the observer exhibits asymptotic convergence. Estimation of monomer concentration, average molecular weight, polydispersity and filtering of temperature in a batch stirred polymerization reactor illustrates the good performance of the observer proposed.