基于支持向量机的可分离非线性动态系统辨识

1、316Vol.31,No.6 200511ACTA AUTOMATICA SINICA November,20051(200030(E-mail:zhangli,ygxiTP18Identication of Separable Variable Nonlinear Dynamical SystemBased on SVMsZHANG Li XI Yu-Geng(Institute of Automation,Shanghai Jiaotong University,Shanghai200030(E-mail:neuluojiaAbstract In this paper,for the ca

2、se that the state variables can be separated from the control variables in a nonlinear dynamic system,an improved regression estimation algorithm based on SVMs is presented and then applied to nonlinear system identication.This kind of learning machines includes two nonlinear functions whose variabl

3、es are the state and the control ones,respectively,and they are used to identify the two nonlinear functions in the separable-variable nonlinear dynamic system.The simulation results validate the eciency of our method.Key words System identication,support vector machine(SVM,regression estimation, ke

4、rnel function11,2.Mercer3.966312( w1 2+ w2 2+Clk=1(k+1+(k+1(3subject to y(k+1f(y(k,u(k +(k+1f(y(k,u(ky(k+1 +(k+1(k+1,(k+1 0,k=1,···,lC(3Wolfe max16967l Testi=1( y iy i2/l Test, y yl Test4.315, 2.12 13(a(b13Table1Three identied systemse(ku(k1.y(k+1=0.3y(k+0.6y(k1+0.6sin(u(k+1,1u(k=sin(

5、2k/2500.3sin(3u(k+0.1sin(5u(k+e(k+10.12.y(k+1=y(ky(k1y(k+2.51+y2(k+u3(k+e(k+12,2u(k=sin(2k/25+0.1sin(2k/1096831N33,40,20,1,l=50000.82861C=100,=0.01,l=1000.4576C=100,=0.01,l=1000.0584K(·,·,K(·,·N33,40,20,1,l=50000.25572C=100,=0.01,l=1000.1494C=100,=0.01,l=1000.0959K(·,·K

6、(·,·N32,40,20,1,l=50000.31293C=10000,=0.01,l=1000.1564C=1000,=0.01,l=1000.0557K(·,·K(·,· (a(b11(a(bFig.1Example1:(aThe identication error curves obtained by three methods.(bOutputs of the original system and the identication model obtained by our method (a(b23(a(bFig.2Example3:(aThe identication error curves obtained by three m