Stochastic gradient algorithm for a dual-rate Box-Jenkins model based on auxiliary model and FIR model简

Based on the work in Ding and Ding （2008）, we develop a modifi ed stochastic gradient （SG） parameter estimation algorithm for a dual-rate Box-Jenkins model by using an auxiliary model. We simplify the complex dual-rate Box-Jenkins model to two fi nite impulse response （FIR） models, present an auxiliary model to estimate the missing outputs and the unknown noise variables, and compute all the unknown parameters of the system with colored noises. Simulation results indicate that the proposed method is effective.     

Stochastic gradient algorithm for a dual-rate Box-Jenkins model based on auxiliary model and FIR model

Based on the work in Ding and Ding(2008),we develop a modifed stochastic gradient(SG)parameter estimation algorithm for a dual-rate Box-Jenkins model by using an auxiliary model.We simplify the complex dual-rate Box-Jenkins model to two fnite impulse response(FIR)models,present an auxiliary model to estimate the missing outputs and the unknown noise variables,and compute all the unknown parameters of the system with colored noises.Simulation results indicate that the proposed method is efective.     

Continuous-time Hammerstein system identification

A continuous-time Hammerstein system, i.e., a system consisting of a nonlinear memoryless subsystem followed by a linear dynamic one, is identified. The system is driven and disturbed by white random signals. The a priori information about both subsystems is nonparametric, which means that functional forms of both the nonlinear characteristic and the impulse response of the dynamic subsystem are unknown. An algorithm to estimate the nonlinearity is presented and its pointwise convergence to the true characteristic is shown. The impulse response of the dynamic part is recovered with a correlation method. The algorithms are computationally independent. Results of a simulation example are given     

Parameter estimation for control systems based on impulse responses

The impulse signal is an instant change signal in very short time. It is widely used in signal processing, electronic technique, communication and system identification. This paper considers the parameter estimation problems for dynamical systems by means of the impulse response measurement data. Since the cost function is highly nonlinear, the nonlinear optimization methods are adopted to derive the parameter estimation algorithms to enhance the estimation accuracy. By using the iterative scheme, the Newton iterative algorithm and the gradient iterative algorithm are proposed for estimating the parameters of dynamical systems. Also, a damping factor is introduced to improve the algorithm stability. Finally, using simulation examples, this paper analyzes and compares the merit and weakness of the proposed algorithms.     

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.     

A new control method of nonlinear systems based on impulseresponses of universal learning networks

A new control method of nonlinear dynamic systems is proposed based on the impulse responses of universal learning networks (ULNs), ULNs form a superset of neural networks. They consist of a number of interconnected nodes where the nodes may have any continuously differentiable nonlinear functions in them and each pair of nodes can be connected by multiple branches with arbitrary time delays. A generalized learning algorithm is derived for the ULNs, in which both the first order derivatives (gradients) and the higher order derivatives are incorporated. One of the distinguished features of the proposed control method is that the impulse response of the systems is considered as an extended part of the criterion function and it can be calculated by using the higher order derivatives of ULNs. By using the impulse response as the criterion function, nonlinear dynamics with not only quick response but also quick damping and small steady state error can be more easily obtained than the conventional nonlinear control systems with quadratic form criterion functions of state and control variables.     

基于Matlab的越野汽车非线性悬架系统仿真

建立了考虑刚度和阻尼非线性的两自由度越野汽车悬架系统的仿真模型。用谐波叠加法构成的路面不平度作为路面激励,并利用半波正弦信号模拟越野汽车通过半圆形路障时的激励,在这些激励下,用数值方法获得了车身加速度,车轮动载,悬架动挠度的响应以及冲击作用下车身加速度的模拟响应。根据随机振动理论谱估计方法,由输入输出信号获得非线性悬架系统传递函数的数值解。以此为基础分析了非线性悬架系统在不同行驶工况下的表现出的传递特性的差异。     

Singular H∞ Suboptimal Control for a Class of Nonlinear Cascade Systems

In the present paper singular state feedback _∞ suboptimal control for a class of nonlinear cascade systems is addressed. Under the assumption that a regular state feedback _∞ suboptimal control problem is solvable for a particular subsystem of the cascade system, an auxiliary nonlinear system is defined. It is shown that a state feedback solution to the singular _∞ suboptimal control problem for the auxiliary system also applies to the original problem. The advantage of the auxiliary problem to the original problem is that the auxiliary penalty variable has lower dimension than the original penalty variable. It is shown how this fact can simplify the problem considerably for the case when the auxiliary system can be strongly input-output decoupled. The theory is applied to a problem of a rigid spacecraft with actuator dynamics. Application to the special case when a subsystem of the nonlinear cascade system is passive is also considered.     

Differential evolution-based nonlinear system modeling using a bilinear series model

This paper presents a new modeling method for nonlinear dynamic systems based on using bilinear series model. Basically, bilinear model is an extension of infinite impulse response (IIR) filter and belongs to the recursive nonlinear system model, i.e., its past output signals will heavily affect the present output. This kind of model can efficiently approximate a large class of nonlinear systems with fewer parameters than other non-recursive models. To adjust the model kernels, we here adopt an evolutionary computation called the differential evolution (DE) algorithm. This algorithm is based on real-valued manipulations and has a good convergence property for finding the global solution or the near global solution of optimized problem. Design steps of DE-based nonlinear system modeling are clearly given in this study. Finally, two kinds of digital systems are illustrated to demonstrate the efficiency of the proposed method.     

Continuous-time Hammerstein system identification from sampled data

A continuous-time Hammerstein system driven by a random signal is identified from observations sampled in time. The sampling may be uniform or not. The a-priori information about the system is nonparametric, functional forms of both the nonlinear characteristic and the impulse response are completely unknown. Three kernel algorithms, one offline and two semirecursive are presented. Their convergence to the true characteristic of the nonlinear subsystem is shown. The distance between consecutive sampling times must not decrease too fast for the algorithms to converge.     

On linear models for nonlinear systems

Best linear time-invariant (LTI) approximations are analysed for several interesting classes of discrete nonlinear time-invariant systems. These include nonlinear finite impulse response systems and a class of nonsmooth systems called bi-gain systems. The Fréchet derivative of a smooth nonlinear system is studied as a potential good LTI model candidate. The Fréchet derivative is determined for nonlinear finite memory systems and for a class of Wiener systems. Most of the concrete results are derived in an ?_∞ signal setting. Applications to linear controller design, to identification of linear models and to estimation of the size of the unmodelled dynamics are discussed.     

On Recursive identification of linear and non-linear systems: case of coloured noise

Recursive identification algorithms based on least square estimation procedure have been presented for both linear and a class of nonlinear systems. The linear system is represented by an impulse response model while the non-linear system is a cascade combination of a. linear part and u zero memory non-linear part. It has been shown that even in the presence of coloured noise, for the model selected, ordinary least square estimation gives unbiased estimates of the system parameters. Results are illustrated through suitable numerical examples.     

Neural filtering method for stationary signal processes

In this paper a new method of neural filtering using artificial neural network systems is presented for the filtering problems of linear and nonlinear, stationary and nonstationary stochastic signals. The neural filter (denoted neurofilter) developed in this paper has either finite impulse response (FIR) structure or infinite impulse response (IIR) structure. The neurofilter differs from the conventional linear digital FIR and IIR filters because the artificial neural network system used in the neurofilter has a nonlinear structure due to the sigmoid function. Numerical studies for the estimation of a second-order Butterworth process are performed by changing the structures of the neurofilter in order to evaluate the performance indices under changes of the output noises or disturbances. The results obtained from these studies verified the capabilities which are essentially necessary for on-line filtering of various stochastic signals.     

Linear approximations of nonlinear FIR systems for separable input processes

Nonlinear systems can be approximated by linear time-invariant (LTI) models in many ways. Here, LTI models that are optimal approximations in the mean-square error sense are analyzed. A necessary and sufficient condition on the input signal for the optimal LTI approximation of an arbitrary nonlinear finite impulse response (NFIR) system to be a linear finite impulse response (FIR) model is presented. This condition says that the input should be separable of a certain order, i.e., that certain conditional expectations should be linear. For the special case of Gaussian input signals, this condition is closely related to a generalized version of Bussgang's classic theorem about static nonlinearities. It is shown that this generalized theorem can be used for structure identification and for the identification of generalized Wiener-Hammerstein systems.     

互相关技术中基于零阶保持器的离散冲激响应模型

利用互相关技术能有效估计线性系统的冲激响应。然而,对于基于数值计算的互相关技术,D/A和A/D转换器的使用必然会带来原理性的误差。该文利用零阶保持器（ZOH）模型从理论上分析了离散时间系统的冲激响应,即它与连续系统冲激响应之间的关系,并给出了时域解析表达式。通过该公式可以直观地把握冲激响应估计的逼真度。     

Extended nonlinear observer canonical form depending on system output and auxiliary state

This paper deals with the problem of transforming a single output nonlinear system with an auxiliary dynamics into an extended nonlinear observer canonical form (ENOCF). The proposed ENOCF depends on system output and auxiliary state, and admits a kind of high-gain observer. We provide two necessary conditions and an equivalent condition for the existence of such a transformation, and then apply the results to the Rössler system as a case study.     

Recursive identification of continuous-time Hammerstein systems

A continuous-time Hammerstein system is identified. The characteristic of its nonlinear subsystem and the impulse response of the dynamic parts are estimated from observations taken at input and output of the whole system. All algorithms are of the on-line type. Their convergence is shown. Results of simulation examples are also presented.     

Adaptive neural network control of uncertain MIMO nonlinear systems with input saturation

In this paper, an adaptive neural network (NN) tracking controller is developed for a class of uncertain multi-input multi-output (MIMO) nonlinear systems with input saturation. Radial basis function neural networks are utilized to approximate the unknown nonlinear functions in the MIMO system. A novel auxiliary system is developed to compensate the effects induced by input saturation (in both magnitude and rate) during tracking control. Endowed with a switching structure that integrates two existing representative auxiliary system designs, this novel auxiliary system improves control performance by preserving their advantages. It provides a comprehensive design structure in which parameters can be adjusted to meet the required control performance. The auxiliary system signal is utilized in both the control law and the neural network weight-update laws. The performance of the resultant closed-loop system is analyzed, and the bound of the transient error is established. Numerical simulations are presented to demonstrate the effectiveness of the proposed adaptive neural network control.     

白噪声驱动的线性系统动态特性测量方法

冲激响应反应了线性系统的内部动态特性。该文详细介绍了系统冲激响应辨识的时域互相关技术。它用白噪声对系统进行驱动,将离散时间线性系统转化为时间序列的ARMA模型,并将基于MA模型的系统辨识问题转化为一个优化问题,以最小二乘标准求解。求解过程利用采样样本估计相关函数,构造对称的Toeplitz矩阵方程,再用迭代的Levinson-Durbin算法解该矩阵方程。最后,文章给出了一个线性系统的测量实例。实验结果表明,该方法能准确的估计线性系统的冲激响应。