给出一种最小二乘支持向量机(Least Square Support Vector Machine,LS-SVM)广义逆内模控制方法。利用LS-SVM辨识这类系统的广义逆,再与原被控系统串联成具有近线性伪线性的开环控制系统,引入内模控制使其变成稳定的闭环控制回路,将这...给出一种最小二乘支持向量机(Least Square Support Vector Machine,LS-SVM)广义逆内模控制方法。利用LS-SVM辨识这类系统的广义逆,再与原被控系统串联成具有近线性伪线性的开环控制系统,引入内模控制使其变成稳定的闭环控制回路,将这种方法应用在球磨机控制系统中。经仿真分析,该方法不依赖于被控系统精确的数学模型,实现了小样本训练的准确辨识,提高了系统的动态响应,并与内模控制相结合,使其闭环控制系统鲁棒稳定性增强。展开更多
Support Vector Machines (SVMs) have been widely used in pattern recognition and have also drawn considerable interest in control areas. Based on a method of least squares SVM (LS-SVM) for multivariate function estimat...Support Vector Machines (SVMs) have been widely used in pattern recognition and have also drawn considerable interest in control areas. Based on a method of least squares SVM (LS-SVM) for multivariate function estimation, a generalized inverse system is developed for the linearization and decoupling control of a general nonlinear continuous system. The approach of inverse modelling via LS-SVM and parameters optimization using the Bayesian evidence framework is discussed in detail. In this paper, complex high-order nonlinear system is decoupled into a number of pseudo-linear Single Input Single Output (SISO) subsystems with linear dynamic components. The poles of pseudo-linear subsystems can be configured to desired positions. The proposed method provides an effective alternative to the controller design of plants whose accurate mathematical model is un- known or state variables are difficult or impossible to measure. Simulation results showed the efficacy of the method.展开更多
We introduce two operator commutators by using different-degree loop algebras of the Lie algebra A1,then under the framework of zero curvature equations we generate two(2+1)-dimensional integrable hierarchies, includi...We introduce two operator commutators by using different-degree loop algebras of the Lie algebra A1,then under the framework of zero curvature equations we generate two(2+1)-dimensional integrable hierarchies, including the(2+1)-dimensional shallow water wave(SWW) hierarchy and the(2+1)-dimensional Kaup–Newell(KN)hierarchy. Through reduction of the(2+1)-dimensional hierarchies, we get a(2+1)-dimensional SWW equation and a(2+1)-dimensional KN equation. Furthermore, we obtain two Darboux transformations of the(2+1)-dimensional SWW equation. Similarly, the Darboux transformations of the(2+1)-dimensional KN equation could be deduced. Finally,with the help of the spatial spectral matrix of SWW hierarchy, we generate a(2+1) heat equation and a(2+1) nonlinear generalized SWW system containing inverse operators with respect to the variables x and y by using a reduction spectral problem from the self-dual Yang–Mills equations.展开更多
文摘给出一种最小二乘支持向量机(Least Square Support Vector Machine,LS-SVM)广义逆内模控制方法。利用LS-SVM辨识这类系统的广义逆,再与原被控系统串联成具有近线性伪线性的开环控制系统,引入内模控制使其变成稳定的闭环控制回路,将这种方法应用在球磨机控制系统中。经仿真分析,该方法不依赖于被控系统精确的数学模型,实现了小样本训练的准确辨识,提高了系统的动态响应,并与内模控制相结合,使其闭环控制系统鲁棒稳定性增强。
基金Project supported by the National Basic Research Program (973) of China (No. 2002CB312200), and the Hi-Tech Research and Devel-opment Program (863) of China (No. 2002AA412010)
文摘Support Vector Machines (SVMs) have been widely used in pattern recognition and have also drawn considerable interest in control areas. Based on a method of least squares SVM (LS-SVM) for multivariate function estimation, a generalized inverse system is developed for the linearization and decoupling control of a general nonlinear continuous system. The approach of inverse modelling via LS-SVM and parameters optimization using the Bayesian evidence framework is discussed in detail. In this paper, complex high-order nonlinear system is decoupled into a number of pseudo-linear Single Input Single Output (SISO) subsystems with linear dynamic components. The poles of pseudo-linear subsystems can be configured to desired positions. The proposed method provides an effective alternative to the controller design of plants whose accurate mathematical model is un- known or state variables are difficult or impossible to measure. Simulation results showed the efficacy of the method.
基金Supported by the National Natural Science Foundation of China under Grant No.11371361the Shandong Provincial Natural Science Foundation of China under Grant Nos.ZR2012AQ011,ZR2013AL016,ZR2015EM042+2 种基金National Social Science Foundation of China under Grant No.13BJY026the Development of Science and Technology Project under Grant No.2015NS1048A Project of Shandong Province Higher Educational Science and Technology Program under Grant No.J14LI58
文摘We introduce two operator commutators by using different-degree loop algebras of the Lie algebra A1,then under the framework of zero curvature equations we generate two(2+1)-dimensional integrable hierarchies, including the(2+1)-dimensional shallow water wave(SWW) hierarchy and the(2+1)-dimensional Kaup–Newell(KN)hierarchy. Through reduction of the(2+1)-dimensional hierarchies, we get a(2+1)-dimensional SWW equation and a(2+1)-dimensional KN equation. Furthermore, we obtain two Darboux transformations of the(2+1)-dimensional SWW equation. Similarly, the Darboux transformations of the(2+1)-dimensional KN equation could be deduced. Finally,with the help of the spatial spectral matrix of SWW hierarchy, we generate a(2+1) heat equation and a(2+1) nonlinear generalized SWW system containing inverse operators with respect to the variables x and y by using a reduction spectral problem from the self-dual Yang–Mills equations.
