一类非线性系统预测控制中的建模问题
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摘要
预测控制,是基于模型的控制方法,但并不拘泥于模型的形式。预测模型的建立是整个预测控制的基础,是预测控制中至关重要的一个环节。由于非线性系统没有统一的模型描述形式,各种非线性系统的预测控制,都是基于不同非线性系统模型描述形式进行的。因此,进行非线性系统预测控制研究,有必要研究预测模型的建立问题。本文研究了一类非线性系统预测控制中的建模问题,提出了一类非线性系统的几种建模方法,以及基于这些建模方法的非线性系统预测控制算法。
给出一类非线性系统的实现简单的多项式逼近的建模方法,在此方法中,将输入输出数据通过拓扑同胚变换,变换到[0,1]区间内,用多项式逼近的方法进行建模,对初始给定的多项式模型,通过反复的参数辨识、去除模型中的冗余项,得到非线性系统的多项式逼近模型,再利用拓扑反变换,将数据还原回原始数据区间。对一类非线性系统,利用多项式逼近的建模方法,用测得的输入输出数据,建立多个不同预报步长的输出非线性预测模型,优化二次性能指标,将问题转化为求解控制量的多元一次方程组问题,将解方程得到的预测控制律与前步预测控制误差做平滑得到控制律,从而得到基于多项式逼近建模的一类非线性系统预测控制算法。
对非线性模糊建模方法进行研究,给出了两种改进的模糊建模方法。在改进的最近邻模糊聚类建模方法中,将最近邻聚类半径和方差参数进行动态更新,使聚类更符合实际情况,从而提高了建模精度。在基于递阶聚类的T-S模糊建模方法中,首先用最近邻聚类求出聚类数与聚类中心,用GK聚类确定前件参数,再用带遗忘因子的最小二乘法进行后件参数辨识,辨识过程中根据规则对模型的贡献的大小,剔除一些对系统模型贡献较小的模糊规则。并在此基础上给出了一种基于改进递阶聚类模糊T-S模型建模方法的模糊预测控制算法,根据预测控制中的预测步长,建立多个包括当前时刻以前的输入输出数据、未来时刻的输入量的模糊预测模型,可以在不求解Diophantine方程的情况下通过最优化性能指标得到预测控制律。
研究一类非线性系统的多层递阶建模及参数预报,通过多层递阶方法建立预测模型,给出了一类非线性系统的多层递阶自适应预测控制算法。此方法不必考虑被控非线性系统的模型具体形式,只是根据系统输入输出,直接用与之等价的时变线性模型代替它。通过参数的在线辨识与预报,实现了单输入单输出非线性系统的自适应预测控制,有着比较广泛的适用性。
针对一类非线性系统,提出一种无模型预测控制方法,将无模型控制中的泛模型思想应用于非线性预测控制。在预测控制中,不对被控系统建立模型,利用输入输出数据辨识泛模型的特征向量,并利用多层递阶的办法对泛模型的特征向量进行预测,从而求得无模型预测控制律。无模型预测控制律中加上功能组合模块将和无模型控制器有着同样的优越性。
Predictive control is a control method based on but not confined by the model. Building prediction model is essential and critical to predictive control. Due to the lack of unified model description, predictive control of various nonlinear systems is based on the model description of different nonlinear systems. Therefore, it is necessary to study modeling in nonlinear system predictive control. Several kinds of modeling method of A Class of nonlinear system are presented in this paper, and based on these non-linear modeling methods, several kinds of predictive control algorithms of nonlinear system are introduced.
A simple polynomial approach for A Class of nonlinear system modeling is presented. By this, the input-output data are firstly changed into [0, 1] by using topological homeomorphism conversion; then an initial polynomial model is selected. The parameters of polynomial model are estimated by using recursion least squares method. A final polynomial model is obtained by repeatedly estimating parameter and eliminating redundant terms. A predictive control algorithm based on polynomial approach modeling is proposed. For nonlinear system, a series of nonlinear output prediction models with different prediction steps are obtained by polynomial approach of nonlinear modeling. Solving predictive control law is turned into solving group of equation by optimizing objective function. The predictive control law is modified by pre-step predictive control error.
Fuzzy modeling method is studied and two kinds of improved fuzzy modeling methods are presented. In improved nearest neighborhood cluster fuzzy modeling, accuracy is achieved by dynamically updating radius of cluster and the variance parameter. In improved T-S fuzzy modeling method, the number of clusters and clustering center are obtained first by improved nearest neighborhood cluster; then, antecedent parameters are obtained by Gustafson-Kessel fuzzy clustering and consequent parameters are identified by least square with forget factor; finally, a model is obtained by acquiring the important rules and removing the less important rules. A fuzzy predictive control method based on improved T-S fuzzy modeling method thus is acquired. A series of predictive model is obtained by improved T-S fuzzy modeling method. The model includes input and output data before current time and future input value. This method does not need to solve Diophantine equation and nonlinear programming.
Research on multi-layer recursive is used in modeling and forecasting of A Class of nonlinear system. A multi-layer recursive adaptive predictive control method is presented for nonlinear discrete system. In this method, nonlinear system is substituted by a time-varying linear system firstly, and then multi-layer recursive is used to identify and to forecast the varied parameters in order to get the predictive output of system model. At last, adaptive predictive control is designed for the original nonlinear system. This method does not need to solve Diophantine equation and does not need to depend on model of nonlinear system.
For A Class of nonlinear system, a model free predictive control is presented. This method does not need modeling in the predictive control. The eigenvector of general model is identified and predicted by multi-layer recursive method. With function combinations, the model free predictive control law has the same advantages as model free control does.
给出一类非线性系统的实现简单的多项式逼近的建模方法,在此方法中,将输入输出数据通过拓扑同胚变换,变换到[0,1]区间内,用多项式逼近的方法进行建模,对初始给定的多项式模型,通过反复的参数辨识、去除模型中的冗余项,得到非线性系统的多项式逼近模型,再利用拓扑反变换,将数据还原回原始数据区间。对一类非线性系统,利用多项式逼近的建模方法,用测得的输入输出数据,建立多个不同预报步长的输出非线性预测模型,优化二次性能指标,将问题转化为求解控制量的多元一次方程组问题,将解方程得到的预测控制律与前步预测控制误差做平滑得到控制律,从而得到基于多项式逼近建模的一类非线性系统预测控制算法。
对非线性模糊建模方法进行研究,给出了两种改进的模糊建模方法。在改进的最近邻模糊聚类建模方法中,将最近邻聚类半径和方差参数进行动态更新,使聚类更符合实际情况,从而提高了建模精度。在基于递阶聚类的T-S模糊建模方法中,首先用最近邻聚类求出聚类数与聚类中心,用GK聚类确定前件参数,再用带遗忘因子的最小二乘法进行后件参数辨识,辨识过程中根据规则对模型的贡献的大小,剔除一些对系统模型贡献较小的模糊规则。并在此基础上给出了一种基于改进递阶聚类模糊T-S模型建模方法的模糊预测控制算法,根据预测控制中的预测步长,建立多个包括当前时刻以前的输入输出数据、未来时刻的输入量的模糊预测模型,可以在不求解Diophantine方程的情况下通过最优化性能指标得到预测控制律。
研究一类非线性系统的多层递阶建模及参数预报,通过多层递阶方法建立预测模型,给出了一类非线性系统的多层递阶自适应预测控制算法。此方法不必考虑被控非线性系统的模型具体形式,只是根据系统输入输出,直接用与之等价的时变线性模型代替它。通过参数的在线辨识与预报,实现了单输入单输出非线性系统的自适应预测控制,有着比较广泛的适用性。
针对一类非线性系统,提出一种无模型预测控制方法,将无模型控制中的泛模型思想应用于非线性预测控制。在预测控制中,不对被控系统建立模型,利用输入输出数据辨识泛模型的特征向量,并利用多层递阶的办法对泛模型的特征向量进行预测,从而求得无模型预测控制律。无模型预测控制律中加上功能组合模块将和无模型控制器有着同样的优越性。
Predictive control is a control method based on but not confined by the model. Building prediction model is essential and critical to predictive control. Due to the lack of unified model description, predictive control of various nonlinear systems is based on the model description of different nonlinear systems. Therefore, it is necessary to study modeling in nonlinear system predictive control. Several kinds of modeling method of A Class of nonlinear system are presented in this paper, and based on these non-linear modeling methods, several kinds of predictive control algorithms of nonlinear system are introduced.
A simple polynomial approach for A Class of nonlinear system modeling is presented. By this, the input-output data are firstly changed into [0, 1] by using topological homeomorphism conversion; then an initial polynomial model is selected. The parameters of polynomial model are estimated by using recursion least squares method. A final polynomial model is obtained by repeatedly estimating parameter and eliminating redundant terms. A predictive control algorithm based on polynomial approach modeling is proposed. For nonlinear system, a series of nonlinear output prediction models with different prediction steps are obtained by polynomial approach of nonlinear modeling. Solving predictive control law is turned into solving group of equation by optimizing objective function. The predictive control law is modified by pre-step predictive control error.
Fuzzy modeling method is studied and two kinds of improved fuzzy modeling methods are presented. In improved nearest neighborhood cluster fuzzy modeling, accuracy is achieved by dynamically updating radius of cluster and the variance parameter. In improved T-S fuzzy modeling method, the number of clusters and clustering center are obtained first by improved nearest neighborhood cluster; then, antecedent parameters are obtained by Gustafson-Kessel fuzzy clustering and consequent parameters are identified by least square with forget factor; finally, a model is obtained by acquiring the important rules and removing the less important rules. A fuzzy predictive control method based on improved T-S fuzzy modeling method thus is acquired. A series of predictive model is obtained by improved T-S fuzzy modeling method. The model includes input and output data before current time and future input value. This method does not need to solve Diophantine equation and nonlinear programming.
Research on multi-layer recursive is used in modeling and forecasting of A Class of nonlinear system. A multi-layer recursive adaptive predictive control method is presented for nonlinear discrete system. In this method, nonlinear system is substituted by a time-varying linear system firstly, and then multi-layer recursive is used to identify and to forecast the varied parameters in order to get the predictive output of system model. At last, adaptive predictive control is designed for the original nonlinear system. This method does not need to solve Diophantine equation and does not need to depend on model of nonlinear system.
For A Class of nonlinear system, a model free predictive control is presented. This method does not need modeling in the predictive control. The eigenvector of general model is identified and predicted by multi-layer recursive method. With function combinations, the model free predictive control law has the same advantages as model free control does.
引文
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