function KineticsEst1_Int_modified_by_Yuezhilan
clear all;clc
format long
tspan=[0,1,2,3,4,5,7,10,15,20,30,45,90,120];
yexp=[0,0.3425,0.61125,0.6125,0.67,0.8025,0.85,0.8375,0.93,0.955,0.95125,0.95375,0.95625,0.96125]';

k0=[1 1];   %%%Çë×¢ÒâÕâÀ³õÖµµÄÑ¡È¡
y0=0.2;
lb=[0 0];
ub=[1000 10];   
yy=[y0 yexp'];

[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
    lsqnonlin(@ObjFunc,k0,lb,ub,[],tspan,y0,yexp);
fprintf('\n\nʹÓú¯Êýlsqnonlin()¹À¼ÆµÃµ½µÄ²ÎÊýֵΪ:\n')
fprintf('\t´ýÄâºÏ²ÎÊý k1 = %.6f\n',k(1))
fprintf('\t´ýÄâºÏ²ÎÊý k2 = %.6f\n',k(2))
fprintf(' \t²Ð²îƽ·½ºÍ= %.6f\n\n',resnorm)
ts=0:1:max(tspan);

[ts ys]=ode45(@KineticsEqs,ts,y0,[],k);
[ttt XXsim] = ode45(@KineticsEqs,tspan,y0,[],k);
y=XXsim(2:end);
xexp=yexp;
R2=1-sum((xexp-y).^2)./sum((xexp-mean(y)).^2);
fprintf('\n\t¾ö¶¨ÏµÊýR-Square = %.6f',R2);
figure(1)
plot(ts,ys,'b',tspan,yy,'or'),legend('¼ÆËãÖµ','ʵÑéÖµ','Location','best');
yr=y-yexp;
figure(2)
plot(tspan(2:end),yr,'r*',[-1 15],[0 0]),axis([-1 15 -0.5 0.5]);
figure(3)
plot(yexp,y,'ro',[21 29],[21 29],'b-');

%---------------------------------------------------------
function f = ObjFunc(k,tspan,y0,yexp)           
[t Xsim] = ode45(@KineticsEqs,tspan,y0,[],k)
ysim = Xsim(2:end);
size(ysim);
size(yexp);
f=ysim-yexp;
%----------------------------------------------------------

function dydt = KineticsEqs(t,y,k)
beta(1)=k(1);
beta(2)=k(2);
dydt =beta(1)*(0.9-y)^beta(2)*(7.5-y);

function KineticsEst1_Int_modified_by_Yuezhilan
clear all;clc
format long
tspan=[0,1,2,3,4,5,7,10,15,20,30,45,90,120];
yexp=[0.3425,0.61125,0.6125,0.67,0.8025,0.85,0.8375,0.93,0.955,0.95125,0.95375,0.95625,0.96125]';

k0=[1 1];   %%%Çë×¢ÒâÕâÀ³õÖµµÄÑ¡È¡
y0=0.2;
lb=[-inf -inf];
ub=[+inf +inf];   
yy=[y0 yexp'];

[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
    lsqnonlin(@ObjFunc,k0,lb,ub,[],tspan,y0,yexp);
fprintf('\n\nʹÓú¯Êýlsqnonlin()¹À¼ÆµÃµ½µÄ²ÎÊýֵΪ:\n')
fprintf('\t´ýÄâºÏ²ÎÊý k1 = %.6f\n',k(1))
fprintf('\t´ýÄâºÏ²ÎÊý k2 = %.6f\n',k(2))
fprintf(' \t²Ð²îƽ·½ºÍ= %.6f\n\n',resnorm)
ts=0:1:max(tspan);

[ts ys]=ode45(@KineticsEqs,ts,y0,[],k);
[ttt XXsim] = ode45(@KineticsEqs,tspan,y0,[],k);
y=XXsim(2:end);
xexp=yexp;
[ttt(2:end) y xexp]
R2=1-sum((xexp-y).^2)./sum((xexp-mean(y)).^2);
fprintf('\n\t¾ö¶¨ÏµÊýR-Square = %.6f',R2);
figure(1)
plot(ts,ys,'b',tspan,yy,'or'),legend('¼ÆËãÖµ','ʵÑéÖµ','Location','best');



%---------------------------------------------------------
function f = ObjFunc(k,tspan,y0,yexp)           
[t Xsim] = ode45(@KineticsEqs,tspan,y0,[],k);
ysim = Xsim(2:end);
size(ysim);
size(yexp);
f=ysim-yexp;
%----------------------------------------------------------

function dydt = KineticsEqs(t,y,k)
beta(1)=k(1);
beta(2)=k(2);
dydt =beta(1)*(0.9-y).^beta(2)*(7.5-y);

2Â¥: Originally posted by ÔÂÖ»À¶ at 2015-06-01 18:52:09
function KineticsEst1_Int_modified_by_Yuezhilan
clear all;clc
format long
tspan=;
yexp=';

k0=;   %%%Çë×¢ÒâÕâÀ³õÖµµÄÑ¡È¡
y0=0.2;
lb=;
ub=;   
yy=;

= ...
    lsqnonlin(@ObjFunc,k0,l ...