NARX model based nonlinear dynamic system identification using low complexity neural networks and robust H∞ filter

This paper proposes NARX (nonlinear autoregressive model with exogenous input) model structures with functional expansion of input patterns by using low complexity ANN (artificial neural network) for nonlinear system identification. Chebyshev polynomials, Legendre polynomials, trigonometric expansions using sine and cosine functions as well as wavelet basis functions are used for the functional expansion of input patterns. The past input and output samples are modeled as a nonlinear NARX process and robust H_∞ filter is proposed as the learning algorithm for the neural network to identify the unknown plants. H_∞ filtering approach is based on the state space modeling of model parameters and evaluation of Jacobian matrices. This approach is the robustification of Kalman filter which exhibits robust characteristics and fast convergence properties. Comparison results for different nonlinear dynamic plants with forgetting factor recursive least square (FFRLS) and extended Kalman filter (EKF) algorithms demonstrate the effectiveness of the proposed approach.     

基于量测迭代更新集合卡尔曼滤波的机动目标跟踪算法

在机动目标跟踪中,用于模型辨识和状态估计的非线性滤波器的合理选择和优化是提升滤波精度的关键.融合量测迭代更新集合卡尔曼滤波和交互式多模型(interacting multiple models,IMM)方法,本文提出了基于量测迭代更新集合卡尔曼滤波的机动目标跟踪算法.通过迭代更新思想的引入构建了一种量测迭代更新下集合卡尔曼滤波的实现结构,并将其作为IMM的模型滤波器实现对于目标运动模式和状态的辨识与估计.针对算法结合过程中滤波精度和计算量的平衡,设计了用于输入交互环节的状态估计样本,同时简化输入交互环节和输出交互环节中滤波误差协方差矩阵的交互过程.理论分析和仿真结果验证了算法的可行性和有效性.     

Output Feedback Adaptive Neural Control Without Seeking SPR Condition

For output‐feedback adaptive control of affine nonlinear systems based on feedback linearization and function approximation, the observation error dynamics usually should be augmented by a low‐pass filter to satisfy a strictly positive real (SPR) condition so that output feedback can be realized. Yet, this manipulation results in filtering basis functions of approximators, which makes the order of the controller dynamics very large. This paper presents a novel output‐feedback adaptive neural control (ANC) scheme to avoid seeking the SPR condition. A saturated output‐feedback control law is introduced based on a state‐feedback indirect ANC structure. An adaptive neural network (NN) observer is applied to estimate immeasurable system state variables. The output estimation error rather than the basis functions is filtered and the filter output is employed to update NNs. Under given initial conditions and sufficient control parameter constraints, it is proved that the closed‐loop system is uniformly ultimately bounded stable in the sense that both the state estimation errors and the tracking errors converge to small neighborhoods of zero. An illustrative example is provided to demonstrate the effectiveness of this approach.     

Grey-box state-space identification of nonlinear mechanical vibrations

The present paper deals with the identification of nonlinear mechanical vibrations. A grey-box, or semi-physical, nonlinear state-space representation is introduced, expressing the nonlinear basis functions using a limited number of measured output variables. This representation assumes that the observed nonlinearities are localised in physical space, which is a generic case in mechanics. A two-step identification procedure is derived for the grey-box model parameters, integrating nonlinear subspace initialisation and weighted least-squares optimisation. The complete procedure is applied to an electrical circuit mimicking the behaviour of a single–input, single–output (SISO) nonlinear mechanical system and to a single–input, multiple–output (SIMO) geometrically nonlinear beam structure.     

Neural Network Adaptive Robust Control Of Siso Nonlinear Systems In A Normal Form

In this paper, performance oriented control laws are synthesized for a class of single‐input‐single‐output (SISO) n‐th order nonlinear systems in a normal form by integrating the neural networks (NNs) techniques and the adaptive robust control (ARC) design philosophy. All unknown but repeat‐able nonlinear functions in the system are approximated by the outputs of NNs to achieve a better model compensation for an improved performance. While all NN weights are tuned on‐line, discontinuous projections with fictitious bounds are used in the tuning law to achieve a controlled learning. Robust control terms are then constructed to attenuate model uncertainties for a guaranteed output tracking transient performance and a guaranteed final tracking accuracy. Furthermore, if the unknown nonlinear functions are in the functional ranges of the NNs and the ideal NN weights fall within the fictitious bounds, asymptotic output tracking is achieved to retain the perfect learning capability of NNs. The precision motion control of a linear motor drive system is used as a case study to illustrate the proposed NNARC strategy.     

一类二次曲面上的参数样条

在空间四个有序数据点所确定的一个二次曲面上,可以构造一类特殊的曲线。给出了四个形状控制因子的有理基函数,以及通过研究其参数间的函数关系定义函数集,构造一类样条曲线,使得通过改变控制因子能任意精确地逼近控制多边形。这类样条曲线端点处满足一定切线方向和有界曲率,容易将它们拼接成一条逼近样条曲线。利用这些样条构造出逼近样条曲面,具有更多的自由度。     

层次泛函网络整体学习算法

文中设计了一类单输人单输出泛函网络与双输人单输出泛函网络作为构造层次泛函网络基本模型,提出了一种层次泛函网络模型,给出了层次泛函网络构造方法和整体学习算法,而层次泛函网络的参数利用解方程组来进行逐层学习．以非线性代数方程组为例,指出人们熟知的一些数学解题方法可以用层次泛函网络来表达,探讨了基于层次泛函网络求解非线性代数方程组学习算法实现的一些技术问题．相对传统方法,层次泛函网络更适合于具有层次结构的应用领域．计算机仿真结果表明,这种层次学习方法具有较快的收敛速度和良好的逼近性能．     

Finite-time command filter-based adaptive tracking control for nonstrict feedback nonlinear systems with full-state restrictions and unmodeled dynamics

The finite-time command filter tracking control for a class of nonstrictly feedback nonlinear systems with unmodeled dynamics and full-state constraints is investigated in this paper. The hyperbolic tangent function is used as a nonlinear mapping technique to solve the obstacle of the full-state constraints. A new adaptive finite time control method is proposed through command filtering reverse engineering, and the shortcomings of the dynamic surface control (DSC) method are overcome by the error compensation mechanism. Dynamic signal is designed to handle dynamical uncertain terms. Normalization signal is designed to handle input unmodeled dynamics. Unknown nonlinear functions are approximated by radial basis function neural networks. Based on the Lyapunov stability theory, it is proved that all signals in the closed-loop system are semi-globally consistent and finally bounded and the output tracking error converges in finite time. Two numerical examples are utilized to verify the effectiveness of the proposed control approach.     

递推更新高斯粒子滤波器

传统高斯粒子滤波算法(Gaussian particle Filter,GPF)中,粒子的重要性密度函数是由高斯滤波器结合当前最新量测来构建的.由于传统高斯滤波器在量测更新阶段直接利用量测对状态进行线性更新,在某些条件下会导致所构建的重要性密度函数并不能很好地近似状态真实分布.为了解决这一问题,结合递推更新的思想,本文推导出了递推更新高斯滤波器(recursive update Gaussian filter,RUGF)的一般结构.并在此基础上,选用RUGF来构建粒子滤波的重要性密度函数,从而提出了基于递推更新的高斯粒子滤波算法(recursive update gaussian particle filter,RUGPF).仿真表明,在非线性系统状态估计问题中,递推更新可以很好的利用量测信息,相比于传统的GPF,本文所提出的RUGPF滤波算法可以提供更高精度的估计结果.     

具有输入约束和输出噪声的不确定系统级联线性自抗扰控制EI北大核心CSCD

针对一类具有输入约束和输出噪声的SISO(Single input single output)不确定非线性系统,提出了一种基于误差补偿和工程滤波的抗饱和级联线性自抗扰控制(Linear active disturbance rejection control,LADRC)方法.首先针对高频量测噪声,分析了线性扩张状态观测器(Linear extended state observer,LESO)对噪声的放大机理及其与观测器增益的定量关系,进而设计了一种基于工程滤波器的级联LADRC方法,在滤除噪声的同时有效补偿了因滤波所造成的输出幅值和相位损失,确保了闭环系统的跟踪精度.然后继续考虑输入饱和的问题,利用LADRC的实时估计/补偿能力,通过将饱和差值信号引入LESO,设计了一种基于误差补偿的抗饱和LADRC方法,有效减小了系统设计控制量,避免了系统长时间陷入饱和.通过实时仿真比较,验证了所提出方法的有效性.     

基于神经网络的周期扰动非线性系统自适应渐近跟踪控制

针对一类具有周期扰动和输入时滞的不确定非线性系统,提出一种基于神经网络的自适应动态面控制方案.将径向基函数神经网络和傅里叶级数展开结合,构造一种混合函数逼近器来逼近系统中未知的周期扰动函数.通过引入一个积分项解决输入时滞问题,同时采用带有非线性滤波器的动态面控制方法,避免自适应反推控制方法中普遍存在的复杂性爆炸问题.所...     

Approximation-theoretic methods for nonlinear deconvolution and inversion

Nonlinear deconvolution and nonlinear inversion are cast as inverse problems in generalized Fock spaces. Generalized Fock spaces, introduced by de Figueiredo and Dwyer in [1], are reproducing kernel Hilbert spaces (RKHSs) of input-output maps represented by Volterra series equipped with an appropriately weighted inner product, the choice of the weights in the inner product depending on the particular problem under consideration. The solution to the nonlinear deconvolution problem presented here is the same as the one obtained previously for the nonlinear system identification problem [1–4]. However, the present solution to the nonlinear inversion problem consists of a new approach, whereby the unknown samples of the input are obtained from the given samples of the output by means of an efficient sequential algorithm. The algorithm is based on a framework which interpolates the input samples by an appropriate spline, and its sequential nature is elicited by the use of a truncated function basis to represent the spline.     

Multidimensional Taylor network adaptive control for MIMO time‐varying uncertain nonlinear systems with noises

In this paper, an adaptive control approach based on the multidimensional Taylor network (MTN) is proposed here for the real‐time tracking control of multiple‐input–multiple‐output (MIMO) time‐varying uncertain nonlinear systems with noises. Two MTNs are used to formulate the optimum control and adaptive filtering approaches. The feed‐forward MTN controller (MTNC) is developed to realize the precise tracking control. The closed‐loop errors between the filtered outputs and expected values are directly chosen as the MTNC's inputs. A valid initial value selection scheme for the weights of the MTNC, which can ensure the initial stability of adaptive process, is introduced. The proposed MTNC can update its weights online according to errors caused by system's uncertain factors, based on stable learning rate. The resilient backpropagation algorithm and the adaptive variable step size algorithm via linear reinforcement are utilized to update the MTNC's weights. The MTN filter (MTNF) is developed to eliminate measurement noises and other stochastic factors. The proposed adaptive MTN filtering system possesses the distinctive properties of the Lyapunov theory–based adaptive filtering system and MTN. Lyapunov function of the filtering errors between the measured values and MTNF's outputs is defined. By properly choosing the weights update law in the Lyapunov sense, the MTNF's outputs can asymptotically converge to the desired signals. The design is independent of the stochastic properties of the input disturbances. Simulation of the MTN‐based control is conducted to test the effectiveness of the presented results.     

Robust Adaptive Neural Network Control For A Class Of Multiple‐Input Multiple‐Output Nonlinear Time Delay System With Hysteresis Inputs And Dynamic Uncertainties

This paper studies an adaptive neural control for nonlinear multiple‐input multiple‐output systems with dynamic uncertainties, hysteresis input, and time delay. The studied systems are composed of N nonlinear time‐delay subsystems and the interconnection terms are contained in every equation of each subsystem. Adaptive neural control algorithms are developed by introducing a well‐defined smooth function. The unknown time‐varying delays and the unmodeled dynamics are dealt with by constructing appropriate Lyapunov–Krasovskii functions and introducing an available dynamic signal. The main advantage of the proposed controllers is that they contain fewer parameter estimates that need to be updated online. Consequently, the accuracy of ultimate tracking errors asymptotically approaches a pre‐defined bound, and all signals in the closed‐loop systems are also ensured to be uniformly ultimately bounded. Finally, a simulation example is provided to illustrate the effectiveness and merits of the proposed adaptive neural network control schemes.     

CNC系统中NURBS曲线插补及相关算法研究

为提高计算机数字控制（CNC）系统的轮廓控制精度,需解决系统控制软件样条直接输出的问题。基于Taylor公式得到了非均匀有理B样条（NURBS）曲线上两个相邻插补点参数间的递推关系。对于NURBS曲线插补过程中需要频繁计算的B样条基函数及其任意阶导数提出了一种分块矩阵连乘积形式的统一计算方法。应用数值计算方法解决了插补过程中曲线长度等的相关计算问题。实例运算表明所提出的方法可以应用到实际CNC系统中。     

Linearized controller design for the output probability density functions of non-Gaussian stochastic systems

1 Introduction There are many practical systems that require the control of the shape of the output probability den- sity function rather than just their mean values and variances. These systems are seen in papermaking processes[1,2], chemical engineering, material science, combustion ?ame distribution systems and food pro- cessing industries. For example, in chemical engineer- ing the control of particle size distribution has al- ways been regarded as an important area of research[3], whilst …     

Fuzzy local linearization and local basis function expansion innonlinear system modeling

Fuzzy local linearization is compared with local basis function expansion for modeling unknown nonlinear processes. First-order Takagi-Sugeno fuzzy model and the analysis of variance (ANOVA) decomposition are combined for the fuzzy local linearization of nonlinear systems, in which B-splines are used as membership functions of the fuzzy sets for input space partition. A modified algorithm for adaptive spline modeling of observation data (MASMOD) is developed for determining the number of necessary B-splines and their knot positions to achieve parsimonious models. This paper illustrates that fuzzy local linearization models have several advantages over local basis function expansion based models in nonlinear system modeling.     

具有未建模动态和输出约束的耦合系统的分散自适应控制

针对一类具有输入、状态未建模动态和非线性输入的耦合系统,提出一种自适应神经网络控制方案.利用径向基函数神经网络逼近未知非线性连续函数;引入动态信号和正则化信号处理状态及输入未建模动态;通过引入非线性映射,将具有时变输出约束的严格反馈系统化为不含约束的严格反馈系统.最后,通过理论分析验证闭环系统中所有信号是半全局一致最终有界的,仿真结果进一步验证了所提出控制方案的有效性.     

Robust adaptive output feedback control of a class of discrete‐time nonlinear systems with nonlinear uncertainties and unknown control directions

In this paper, robust adaptive output feedback control is studied for a class of discrete‐time nonlinear systems with functional nonlinear uncertainties of the Lipschitz type and unknown control directions. In order to construct an output feedback control, the system is transformed into the form of a nonlinear autoregressive moving average with eXogenous inputs (NARMAX) model. In order to avoid the noncausal problem in the control design, future output prediction laws and parameter update laws with the dead‐zone technique are constructed on the basis of the NARMAX model. With the employment of the predicted future outputs, a constructive output feedback adaptive control is proposed, where the discrete Nussbaum gain technique and the dead‐zone technique are used in parameter update laws. The effect of the functional nonlinear uncertainties is compensated for, such that an asymptotic tracking performance is achieved, whereas other signals in the closed‐loop systems are guaranteed to be bounded. Simulation studies are performed to demonstrate the effectiveness of the proposed approach. Copyright © 2012 John Wiley & Sons, Ltd.