基于非光滑神经网络的X-Y定位平台系统模型辨识

本文首先对X-Y定位平台系统的组成及模型的建立作了简单描述,接着,针对X-Y定位平台中存在的载荷以及摩擦参数的不确定性问题,提出了一种基于改进神经网络结构来对X-Y定位平台不确定性非线性系统的辨识的方法.采用非光滑神经网络来对不确定非线性系统建立模型.结果表明该方法能够对复杂的非线性系统进行辨识,比一般的神经网络具有较高的辨识精度,且具有良好的泛化性能.这种方法可以应用到工业过程实际系统中.     

基于混合最小二乘支持向量机网络模型的非线性系统辨识

针对基于输入输出数据的非线性系统辨识问题,提出一种新的混合最小二乘支持向量机(LS-SVMs)网络模型及相应的学习算法.该算法将系统的辨识问题动态自适应的划分为若干子问题,将支持向量机(SVM)用于各子模块辨识;通过分析模型的统计学特性,给出基于整体框架优化的系统参数辨识方法.针对系统中参数相关联的特性,采用期望条件最大化(ECM)算法对其进行条件辨识,同时结合正则化理论和最小二乘法,保证各专家模块的结构风险最小化辨识原则.试验结果表明,该方法兼具良好的辨识精度和泛化性能.     

l 1-l 1双范数的最优下边界回归模型辨识

考虑到来自传感器测量数据、模型结构以及参数的不确定性等因素,建模由这些因素导致的下边界模型尤为重要。通过将结构风险最小化理论与逼近误差最小化思想相结合,提出了${\ell _1} - {\ell _1}$ 双范数的最优下边界回归模型建模方法。首先,确定满足下边界回归模型的约束条件。其次,将结构风险的${\ell _2}$范数转化为简单的${\ell _1}$范数优化问题,并将回归模型与实际测量数据之间的逼近误差的${\ell _1}$范数融合到结构风险的${\ell _1}$范数优化问题,再应用较简单的线性规划对双范数的优化问题进行求解获取模型参数。最后,通过来自测量数据以及模型参数不确定性的实验分析,论证了提出方法的最优性,体现在:下边界模型的建模精度通过逼近误差的${\ell _1}$范数得到保证;模型结构复杂性在结构风险的${\ell _1}$范数优化条件下得到有效控制,进而提高其泛化性能。     

自组织区间二型模糊神经网络及其自适应学习算法

针对复杂不确定非线性系统的辨识问题,提出一种基于聚类的自组织区间二型模糊神经网络学习算法.首先采用具有两个不同加权参数的FCM算法对输入数据进行划分来获取规则前件的不确定均值,同时结合聚类有效性标准确定模糊规则数目,从而自动完成神经网络的结构辨识和规则前件参数辨识;随后给出了基于梯度下降法和Lyapunov函数稳定收敛定理的规则后件权向量学习速率的自适应学习算法.通过非线性系统辨识实例,验证了该算法与其他方法相比具有更快的收敛速度和更高的逼近精度;并且利用该算法建立了某市电力短期负荷预测模型,结果表明该模型具有较高的预测精度,泛化性能更佳.     

非最小相位SIMO系统的盲辨识方法

提出一种非最小相位SIMO系统的盲辨识方法.SIMO系统的多个输出可重新组合为具有循环平稳特性的输出序列,利用信号子空间与噪声子空间正交的特性,可求解系统的模型参数.该方法能辨识最小相位对象的结构参数,对非最小相位对象以及具有无限冲击响应的对象同样有效.该方法运算复杂度低,辨识速度快.仿真结果验证了其有效性.     

未知参数非线性系统的自适应广义预测控制

研究非线性系统的稳定性和跟踪优化问题,针对未知参数非线性系统的参数辨识和输出跟踪问题,给出参数自适应广义预测控制方法,为使辨识模型能实时反映被控对象特性以及输出对设定值的跟踪有较高精度.提出将非线性系统转化为受控自回归滑动平均模型,根据输入输出数据辨识模型参数.采用广义预测控制滚动优化的策略得出最优控制律,将最优控制律作用于对象实现非线性系统的优化控制以及系统输出对设定值的跟踪控制.明显克服了自适应控制对模型精度要求高的缺陷且具有在线辨识,滚动优化的特点.最后,通过仿真实例验证了方法的有效性.     

PSO并行优化LSSVR非线性黑箱模型辨识

针对非线性黑箱系统辨识中存在不确定性、高阶次,采用常规辨识方法建立其精确数学模型十分困难等问题,提出一种基于自适应粒子群算法的最小二乘支持向量机回归(PSO-LSSVR)非线性系统辨识方法.该方法采用2组自适应粒子群算法并行计算模型,分别利用自适应粒子群算法对LSSVR中的参数进行自动选取和矩阵迭代求解,既克服了传统LSSVR参数难以确定的缺点,提高了辨识精度,同时避免了复杂矩阵求逆运算,加快了计算速度.将该方法应用于船舶操纵性模型非线性系统辨识,仿真结果表明,由该方法得到的LSSVR能够有效地对系统进行建模,仿真精度高,结构简单,具有一定的理论推广意义.     

T-S模型的遗传算法和支持向量机辨识

基于非线性系统的输入输出数据,辩识对象的T-S模型.提出基于遗传算法和最小二乘支持向量机的辨识方法,利用遗传算法聚类进行结构辨识,每个类代表一条规则,规则数等于类数量,类中心作为该规则的隶属度函数中心类数;同时考虑模型辨识精度,实现全局优化;参数辨识采用基于结构风险最小化的最小二乘支持向量机方法,综合考虑模型复杂度和辨识误差.仿真结果证明了算法的有效性,辨识精度高,泛化能力强.     

基于相关向量机的非线性动态系统辨识

基于具有核函数不用满足Mercer条件、相关向鼍自动确定及核函数少特点的稀疏贝叶斯的相关向量机核学习方法,提出了平滑先验条件约束的相关向量机的学习方法,采用稀疏贝叶斯模型的最大边缘似然算法加快了求解相关向量机的向量,并采取交叉验证法确定其核参数提高了相关向量机辨识的泛化性.该方法避免了支持向量机的非线性系统辨识的模型结构难于确定的问题,与支持向量机辨识方法相比较,辨识的模型结构更简洁.仿真表明,该方法应用于非线性动态系统的辨识,具有良好的效果.     

基于脉冲响应的输出误差模型的辨识

基于系统脉冲响应参数, 利用相关分析方法, 提出了一种辨识输出误差模型参数的方法. 该方法是利用有限脉冲响应模型逼近输出误差模型, 通过依次递增脉冲响应参数的数目N来提高逼近精度. 理论分析表明, 只要N足够大, 模型的辨识精度可以满足实际要求. 提出的辨识方法可以在假设阶次N =1的条件下, 依次递增计算N较大时的脉冲响应参数和目标函数值, 从而根据脉冲响应确定系统的参数. 仿真试验说明提出的方法估计输出误差模型的参数是有效的.     

Interval regression analysis using quadratic loss support vector machine

Support vector machines (SVMs) have been very successful in pattern recognition and function estimation problems for crisp data. This paper proposes a new method to evaluate interval linear and nonlinear regression models combining the possibility and necessity estimation formulation with the principle of quadratic loss SVM. This version of SVM utilizes quadratic loss function, unlike the traditional SVM. For data sets with crisp inputs and interval outputs, the possibility and necessity models have been recently utilized, which are based on quadratic programming approach giving more diverse spread coefficients than a linear programming one. The quadratic loss SVM also uses quadratic programming approach whose another advantage in interval regression analysis is to be able to integrate both the property of central tendency in least squares and the possibilistic property in fuzzy regression. However, this is not a computationally expensive way. The quadratic loss SVM allows us to perform interval nonlinear regression analysis by constructing an interval linear regression function in a high dimensional feature space. The proposed algorithm is a very attractive approach to modeling nonlinear interval data, and is model-free method in the sense that we do not have to assume the underlying model function for interval nonlinear regression model with crisp inputs and interval output. Experimental results are then presented which indicate the performance of this algorithm.     

Non-Mercer hybrid kernel for linear programming support vector regression in nonlinear systems identification

As a new sparse kernel modeling method, support vector regression (SVR) has been regarded as the state-of-the-art technique for regression and approximation. In [V.N. Vapnik, The Nature of Statistical Learning Theory, second ed., Springer-Verlag, 2000], Vapnik developed the ?-insensitive loss function for the support vector regression as a trade-off between the robust loss function of Huber and one that enables sparsity within the support vectors. The use of support vector kernel expansion provides us a potential avenue to represent nonlinear dynamical systems and underpin advanced analysis. However, in the standard quadratic programming support vector regression (QP-SVR), its implementation is often computationally expensive and sufficient model sparsity cannot be guaranteed. In an attempt to mitigate these drawbacks, this article focuses on the application of the soft-constrained linear programming support vector regression (LP-SVR) with hybrid kernel in nonlinear black-box systems identification. An innovative non-Mercer hybrid kernel is explored by leveraging the flexibility of LP-SVR in choosing the kernel functions. The simulation results demonstrate the ability to use more general kernel function and the inherent performance advantage of LP-SVR to QP-SVR in terms of model sparsity and computational efficiency.     

H∞ output tracking control of uncertain and disturbed nonlinear systems based on neural network model

The work presented in this paper seeks to address the tracking problem for uncertain continuous nonlinear systems with external disturbances. The objective is to obtain a model that uses a reference-based output feedback tracking control law. The control scheme is based on neural networks and a linear difference inclusion (LDI) model, and a PDC structure and H_∞ performance criterion are used to attenuate external disturbances. The stability of the whole closed-loop model is investigated using the well-known quadratic Lyapunov function. The key principles of the proposed approach are as follows: neural networks are first used to approximate nonlinearities, to enable a nonlinear system to then be represented as a linearised LDI model. An LMI (linear matrix inequality) formula is obtained for uncertain and disturbed linear systems. This formula enables a solution to be obtained through an interior point optimisation method for some nonlinear output tracking control problems. Finally, simulations and comparisons are provided on two practical examples to illustrate the validity and effectiveness of the proposed method.     

Identification of dynamical systems with a robust interval fuzzy model

In this paper we present a new method of interval fuzzy model identification. The method combines a fuzzy identification methodology with some ideas from linear programming theory. On a finite set of measured data, an optimality criterion that minimizes the maximal estimation error between the data and the proposed fuzzy model output is used. The idea is then extended to modelling the optimal lower and upper bound functions that define the band that contains all the measurement values. This results in a lower and an upper fuzzy model or a fuzzy model with a set of lower and upper parameters. The model is called the interval fuzzy model (INFUMO). The method can be used when describing a family of uncertain nonlinear functions or when the systems with uncertain physical parameters are observed. We believe that the fuzzy interval model can be very efficiently used, especially in fault detection and in robust control design.     

PID Control of Planar Nonlinear Uncertain Systems in the Presence of Actuator Saturation

This paper investigates PID control design for a class of planar nonlinear uncertain systems in the presence of actuator saturation. Based on the bounds on the growth rates of the nonlinear uncertain function in the system model, the system is placed in a linear differential inclusion. Each vertex system of the linear differential inclusion is a linear system subject to actuator saturation. By placing the saturated PID control into a convex hull formed by the PID controller and an auxiliary linear feedback law, we establish conditions under which an ellipsoid is contractively invariant and hence is an estimate of the domain of attraction of the equilibrium point of the closed-loop system. The equilibrium point corresponds to the desired set point for the system output. Thus, the location of the equilibrium point and the size of the domain of attraction determine, respectively, the set point that the output can achieve and the range of initial conditions from which this set point can be reached. Based on these conditions, the feasible set points can be determined and the design of the PID control law that stabilizes the nonlinear uncertain system at a feasible set point with a large domain of attraction can then be formulated and solved as a constrained optimization problem with constraints in the form of linear matrix inequalities (LMIs). Application of the proposed design to a magnetic suspension system illustrates the design process and the performance of the resulting PID control law.      

确定学习与基于数据的建模及控制

确定学习运用自适应控制和动力学系统的概念与方法, 研究未知动态环境下的知识获取、表达、存储和利用等问题. 针对产生周期或回归轨迹的连续 非线性动态系统, 确定学习可以对其未知系统动态进行局部准确建模, 其基本要 素包括: 1)使用径向基函数(Radial basis function, RBF)神经网络; 2)对于周期(或回归)状态轨迹 满足部分持续激励条件; 3)在周期(或回归)轨迹的邻域内实现对非线性系统动态的局部准确神经网络逼近(局部准确建模); 4)所学的知识以时不变且空间分布的方式表达、以常值神经网络权值的方式存储, 并可在动态环境下用于动态模式的快速识别或者闭环神经网络控制. 本文针对离散动态系统, 扩展了确定学习理论, 提出一个根据时态数据序列对离散动态系统进行建模与控制的框架. 首先, 运用确定学习原理和离散系统的自适应辨识方法, 实现对产生时态数据的离散非线性系统的未知动态进行局部准确的神经网络建模, 并利用此建模结果对时态数据序列进行时不变表达. 其次, 提出时态数据序列的基于动力学的相似性定义, 以及对离散动态系统产生的时态数据序列(亦可称为动态模式)进行快速识别方法. 最后, 针对离散非线性控制系统, 实现了基于时态数据序列对控制系统动态的闭环辨识(局部准确建模). 所学关于闭环动态的知识可用于基于模式的智能控制. 本文表明确定学习可以为时态数据挖掘的研究提供新的途径, 并为基于数据的建模与控制等问题提供新的研究思路.     

Interval Fuzzy Model Identification Using$l_infty$-Norm

In this paper, we present a new method of interval fuzzy model identification. The method combines a fuzzy identification methodology with some ideas from linear programming theory. We consider a finite set of measured data, and we use an optimality criterion that minimizes the maximum estimation error between the data and the proposed fuzzy model output. The idea is then extended to modeling the optimal lower and upper bound functions that define the band which contains all the measurement values. This results in lower and upper fuzzy models or a fuzzy model with a set of lower and upper parameters. The model is called the interval fuzzy model (INFUMO). We also showed that the proposed structure uniformly approximates the band of any nonlinear function. The interval fuzzy model identification is a methodology to approximate functions by taking into account a finite set of input and output measurements. This approach can also be used to compress information in the case of large amount of data and in the case of robust system identification. The method can be efficiently used in the case of the approximation of the nonlinear functions family. If the family is defined by a band containing the whole measurement set, the interval of parameters is obtained as the result. This is of great importance in the case of nonlinear circuits' modeling, especially when the parameters of the circuits vary within certain tolerance bands     

Response modeling methodology (RMM)—maximum likelihood estimation procedures

Response modeling methodology (RMM) is a new approach for empirical modeling. ML estimation procedures for the RMM model are developed. For relational modeling, the RMM model is estimated in two phases. In the first phase, the structure of the linear predictor (LP) is determined and its parameters estimated. This is accomplished by combining canonical correlation analysis with linear regression analysis. The former procedure is used to estimate coefficients in a Taylor series approximation to an unspecified response transformation. Canonical scores are then used in the latter procedure as response values in order to estimate coefficients of the LP. In the second phase, the parameters of the RMM model are estimated via ML, given the LP estimated earlier. For modeling random variation, it is assumed that the LP is constant and a new simple percentile-based estimating procedure is developed. The new estimation procedures are demonstrated for some published data.     

Deterministic and stochastic model based run-to-run control for batch processes with measurement delays of uncertain duration

A novel run-to-run control algorithm integrating deterministic and stochastic model based control is developed for batch processes with measurement delays of uncertain duration. This control algorithm is referred to as deterministic and stochastic model based control (DSMBC). The deterministic component responds quickly to deterministic changes while the stochastic component minimizes the effects arising from measurement delays of uncertain duration. The deterministic component uses a linear process model with parameters that are updated online. The stochastic component uses an error probability density function (PDF) to characterize the effects due to measurement delays and this error PDF is determined from deviations between the set-point and the available process output. To integrate the two control algorithms, the control input is determined by minimizing the weighted sum of the predicted error from the deterministic model and the information entropy of the error probability density distribution. Using a simulated setting where the rate of chemical vapor deposition is controlled, the performance of the proposed DSMBC is shown to be superior to that of EWMA.     

Intuitionistic fuzzy optimization technique for solving multi-objective reliability optimization problems in interval environment

In designing phase of systems, design parameters such as component reliabilities and cost are normally under uncertainties. This paper presents a methodology for solving the multi-objective reliability optimization model in which parameters are considered as imprecise in terms of triangular interval data. The uncertain multi-objective optimization model is converted into deterministic multi-objective model including left, center and right interval functions. A conflicting nature between the objectives is resolved with the help of intuitionistic fuzzy programming technique by considering linear as well as the nonlinear degree of membership and non-membership functions. The resultants max–min problem has been solved with particle swarm optimization (PSO) and compared their results with genetic algorithm (GA). Finally, a numerical instance is presented to show the performance of the proposed approach.