基于最小二乘支持向量机的非线性广义预测控制

太原理工大学 硕士学位论文 基于最小二乘支持向量机的非线性广义预测控制 姓名：程萍 申请学位级别：硕士 专业：@ 指导教师：李国勇 20100301
太原理工大学硕士研究生论文
基于最小二乘支持向量机的非线性广义预测控制
摘 要
工业生产过程通常具有非线性、不确定性和时变性等特点，而传统控 制理论是以对象的精确数学模型为基础，使得要建立精确的解析模型十分 困难，因此导致控制效果不够理想。为了克服这些困难，预测控制作为一 种新型的控制算法引起了国内外控制理论界的广泛重视。预测控制是基于 预测模型、滚动优化和反馈校正等的一种控制策略，因而具有控制性能好、 鲁棒性强、对模型精确性要求不高等特点。 针对工业过程中普遍存在的非线性被控对象，本文提出一种基于最小 二乘支持向量机的非线性广义预测控制算法。 广义预测控制(GPC)是由 Clarke 等人提出的由经典的最小方差控制 和自适应控制发展而来的自适应预测控制算法，该算法是以传统的受控自 回归积分滑动平均（CARIMA）模型为基础，适用于时滞和非最小相位对 象，并改善了控制性能和模型失配的鲁棒性，采用了长时段的优化性能指 标，具有较强的鲁棒性和对模型要求低等特点。 目前基于线性预测模型的广义预测控制方法已成功的应用于工业控制 中，而基于非线性预测模型的广义预测控制，要求控制器在每个采样周期 必须求解一个非线性规划问题，该问题规模与预测模型的参数有关。由于 对非线性系统建模以及在线滚动优化方面存在困难，目前还仅是一个开放 的课题。 目前常用的非线性预测模型包括神经网络、模糊模型等，其学习算法
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太原理工大学硕士研究生论文
least squares support vector machine (LS-SVM) method, which change inequality constraints into equality constraints, the optimization problem into a linear equation, bias in a square into two parties of experience in risk, LS-SVM overcome the classic quadratic programming method for solving support vector machines curse of dimensionality problem, and has a good robustness, suitable for large-scale computing. So use LS-SVM as nonlinear predictive model have more advantages. This thesis will use LS-SVM model and simulate to nonlinear system, and comparison with BP neural network, the simulate results show that LS-SVM has the same model precision and high generalization ability to BP neural network. Then I use GPC carry through predictive control to LS-SVM predictive model and BP neural network, simulate results that the algorithm propose by this thesis have good performance to nonlinear system. Then I use GPC based on LS-SVM to predictive and simulate to a issue of typical strongly nonlinear systems, continuous stirred tank reactor CSTR. the simulation results present that the generalized predictive control algorithm proposed in this paper which based on the least squares support vector machine has a good validity. KEY WORDS: nonlinear system，GPC，LSSVM，LS-SVM toolbox，CSTR
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太原理工大学硕士研究生论文
GENERALIZED PREDICTIVE CONTROL ALGORITHM BASED ON LEAST SQUARES SUPPORT MACHINES
ABSTRACT
A large number of industrial produce processes have a nonlinear, uncertain and time-varying characteristics, however the tradition control theories established by precise mathematic model of the plants, so that it is difficult to establish a precise analytical model, lead to effects of control is not well. In order to overcome those problems, Model Predictive Control (MPC) as a newly control arithmetic arouse widely recognition of domestic and foreign control theory. MPC is based on control strategies of forecasting model, rolling optimization and feedback correction, so it has a good controllability, robustness. Aim at nonlinear decontrolled plants at large exist in industrial processes, this thesis bring forward arithmetic of nonlinear generalized predictive control algorithm based on least squares support vector machines. Generalized predictive control (GPC), aroused by Clarke etc, is a adaptive predictive control algorithm which developed by traditional minimum variance control and adaptive control, GPC is Based on traditional controlled auto-regressive integrated moving average (CARIMA) model, hold true time delay and non-minimum phase object, and improve control performance and
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太原理工大学硕士研究生论文
都是基于经验风险最小化原理，有一些不易解决的难题，如难以确定神经 网络的隐含层节点数、存在过学习现象，训练过程存在局部极小问题等。 近年来由 Vapnik 等人提出的支持向量机（SVM）成为对非线性系统建模的 热点，SVM 是基于统计学习理论的 VC 维理论和结构风险最小化原理，有 效的解决了过学习问题，与神经网络和模糊控制相比，SVM 具有可以自动 设计模型复杂度和泛化能力高等特点，训练算法中不存在局部极小值，可 以很好逼近非线性对象模型。但当训练样本过多时就导致维数灾难。 Suykens J.A.K 在标准 SVM 的目标函数中增加了误差平方和项， 提出最小二 乘支持向量机（LS-SVM）方法，LS-SVM 克服了经典二次规划方法求解支 持向量机的维数灾难问题，具有良好的鲁棒性，适合大规模运算。所以将 LS-SVM 作为非线性预测模型方面更具有优势。 本文将用最小二乘支持向量机对非线性系统进行建模仿真， 并与 BP 神 经网络进行仿真对比， 仿真结果证明最小二乘支持向量机具有和 BP 神经网 络同样好的建模精度和泛化能力。然后用广义预测控制算法对 LS-SVM 预 测模型和 BP 神经网络预测模型进行预测控制， 仿真结果证明本文提出的算 法对非线性系统有很好的控制效果。 最后在一个典型性强非线性系统连续搅拌槽反应器 CSTR 用本文提出 的基于最小二乘支持向量机的非线性广义预测控制进行实验研究，仿真结 果验证了本文提出的基于最小二乘支持向量机的广义预测控制算法的有效 性。 广义预测控制， 支持向量机， 最小二乘支持向量机 连 关键字：非线性系统， 续搅拌槽反应器 CSTR
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太原理工大学硕士研究生论文
robustness of model unmatched, and use long periods optimize performance cost, have characteristics of strong robustness and low request to model. Now , GPC based on linear predictive model is successfully used in industrial control, but GPC based on nonlinear predictive model, require controller resolve a nonlinear programming problem at every sampling period, which size is relate to parameters of predictive model。Due to the difficulties in modeling to nonlinear system and on-line rolling optimization, this problem is still only a open issue. Now commonly used non-linear predictive models, include neural networks fuzzy models and so on, which learning algorithms are based on empirical risk minimization principle. But there are still some difficult problems to solve, such as difficult to determine the hidden layer nodes of neural networks, the phenomenon of over fitting, local minimum problems in the training process and so on. Recently Vapnik and others propose support vector machine (SVM) become hotspot of nonlinear modeling, SVM is based on VC dimension theory of statistical learning theory and structural risk minimization principle, SVM Characteristics of automatically design model with a complexity and high generalization ability, training algorithm don’t have local minimum problem, and have good effect to approximation to nonlinear plant model. But with the increasing of training samples, SVM will be faced with the curse of dimensionality, leading to no training. With an increase of the error sum of squares of items in the standard SVM objective function, Suykens JAK propose