保精度-稀疏特性核回归模型的非线性动态系统辨识  

Kernel Regression Model Guaranteed by Identifying Accuracy and Model Sparsity for Nonlinear Dynamic System Identification

作　　者：刘小雍 方华京 LIU Xiao-yong;FANG Hua-jing(College of Engineering and Technology,Zunyi Normal College,Zunyi 563002,China;School of Automation,Huazhong University of Science&Technology,Wuhan 430074,China)

机构地区：[1]遵义师范学院工学院,遵义563002 [2]华中科技大学自动化学院,武汉430074

出　　处：《科学技术与工程》2020年第19期7804-7814,共11页Science Technology and Engineering

基　　金：国家自然科学基金(61473127);贵州省科学技术项目(黔科合基础[2018]1179号);贵州省教育厅青年项目(黔教合KY字[2016]254);贵州省千层次创新人才项目(遵市科合人才[2017]19号)。

摘　　要：针对一组有限测量数据的非线性动态系统建模方法存在模型结构复杂且易出现过拟合等问题,从建模精度及模型稀疏特性出发,提出了保精度-稀疏特性的核回归模型用于辨识非线性动态系统。该方法将逼近误差的L∞范数思想与结构风险最小化理论相结合,建立求解非线性动态系统所对应的核回归模型优化问题,再应用较简单的线性规划对其求解。提出的方法具有如下三个显著特性:①应用逼近误差的L∞范数最小化可保证非线性动态系统的辨识精度;②引入支持向量回归架构下的结构风险L1范数对模型结构复杂性进行有效控制可保证模型稀疏特性;③模型的泛化性能可通过提出的方法从建模精度与模型稀疏特性之间取其平衡。最后,通过实验分析论证了提出方法在辨识非线性动态系统上的保精度-稀疏特性的合理性与优越性。The conventional nonlinear dynamic system modeling approaches from a finite set of measured data is not prone to control the model structure complexity, and those methods can also lead to over-fitting problems. To deal with this, a kernel regression model guaranteed by identifying accuracy and model sparsity was proposed to model nonlinear dynamic system. From the aspects of dominating the model structure complexity and improving the identification accuracy, the proposed method combined structural risk minimization theory with some ideas from L∞-norm on approximation error minimization, and constructed the optimization problem of kernel regression model corresponding to nonlinear dynamic system. Following that, the optimization could be solved by the simpler linear programming. The method had three remarkable features. Firstly, the identifying accuracy was guaranteed by the L∞-norm minimization on approximation error. Secondly, the model structural complexity was under control by introducing L1-norm on structural risk within the framework of support vector regression(SVR) to guarantee the model sparsity. Thirdly, the optimality of the proposed method realized the equilibrium between the identifying accuracy and sparseness. Finally, rationalities and superiorities of the proposed method in identifying nonlinear dynamic system were demonstrated by experiments.

关 键 词：泛化性能 辨识精度 稀疏特性 L∞范数逼近误差 L1范数结构风险 线性规划 

分 类 号：TP391.9[自动化与计算机技术—计算机应用技术]