The Application Of SVR And K-LSE In System Identification

Support Vector Machines is a new kind of learning technique which is developed in the middle of 90's. It is based on statistical learning theory. It aims at studying the statistical regulation and learning methods under small samples conditions. SVM has many merits comparing to the tradition statistics premised by enough samples. It can obtain ideal effect under limited samples and solve many practical problems characterized by small sample, nonlinearity, high dimension and local minima becoming a hot spot.System identification with widely applied fields is a very important part of modern control theory. The application in linear systems of tradition methods of systems identification such as maximum likelihood, least square method has been mature. But it is impossible to depict the future of the subjects with apparent nonlinearity through linear model. The neural network also has many insufficiencies [ 25 - 29]. We propose K-LSE operation, directed towards the merits and shortcomings of SVM and LSE.First of all, this paper systematically introduce the basic principles of statistical learning theory, place extra emphasis on the kernel theory of SVM. Secondly, we discuss Least Square Estimation theory, propose K-LSE operation based on the kernel theory of SVM and give its geometric significance. In fact, it is a combination of SVM and LSE. We also confirm its effectiveness in function-fitting through simulation experiment.Finally, we propose a new operation—K-LSE operation toward to the system identification a common issue. Moreover, we use the simulation experiment to show the functions of K-LSE in realizing the merits and overcoming the shortcomings in dynamical system identification, thereby, illustrating its superiority comparing to standard SVR and classical LSE.