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СµÜ×î½ü¸ÕѧϰÓÃmatlabÄâºÏ²ÎÊý£¬µ«±àдÍêÔËÐÐÏÔʾInitial point is a local minimum.µÃµ½µÄkֵΪk0£¬Çó¸øÎ»´óÉñ¸øÖ¸µãÒ»ÏÂÔõô½â¾öÕâÖÖÎÊÌ⣡¼±Çó£¬ÐÂÈËɶҲ²»¶®°¡£¡ÏÈÔÚ´Ëл¹ýÀ²£¡
function zixie
clear all;
clc;
data=[0 8.32 0;
    1 7.37 0.211;
    2 6.74 0.738;
    3 5.92 1.106;
    4 5.68 1.296;
    5 5.01 1.583;
    6 6.09 1.364;
    8 5.35 1.84;
    10 4.99 2];
x0=[8.32 0];
k0=[10 10 10 10 10 ];
lb=[0 0 0 0 0];
ub=[+inf +inf +inf +inf +inf];
yexp=data(:,2:3);
[k,resnorm,residual,exitflag,output,lambda,jacobin]=lsqnonlin(@objFunc1,k0,lb,ub,[],x0,yexp)
fprintf('\tk1=%.4\n',k(1)),
fprintf('\tk2=%.4\n',k(2)),
fprintf('\tk3=%.4\n',k(3)),
fprintf('\tk4=%.4\n',k(4)),
fprintf('\tk5=%.4\n',k(5))
function f=objFunc1(k,x0,yexp)
tspan=[0 1 2 3 4 5 6 8 10];
[t x]=ode45(@funceqs,tspan,x0,[],k);
y(:,1)=x(:,1);
y(:,2)=x(:,2);
f1=y(:,1)-yexp(:,1);
f2=y(:,2)-yexp(:,2);
f=[f1;f2];
function dxdt=funceqs(t,x,k)
dx1dt=-k(1)*k(2)*x(1)*sqrt(k(3)*x(2))/(k(1)+k(2)*x(1))-k(4)*k(5)*x(2);
dx2dt=k(1)*k(2)*x(1)*sqrt(k(3)*x(2))/(k(1)+k(2)*x(1))+k(5)*x(2);
dxdt=[dx1dt;dx2dt];

Initial point is a local minimum.


Optimization completed because the size of the gradient at the initial point
is less than the default value of the function tolerance.


<stopping criteria details>
k =

    10   10   10    10    10
Optimization completed: The final point is the initial point.
The first-order optimality measure, 0.000000e+00, is less than
options.TolFun = 1.000000e-06.

Optimization Metric                                   Options
relative first-order optimality =   0.00e+00         TolFun =   1e-06 (default)

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dx1dt=-k1*k2*x1*sqrt(k3*x2)/(k1+k2*x1)-k4*k5*x2;
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dx1dt=-x1*sqrt(x2)/(k1+k2*x1)-k4*k5*x2;
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dx1dt=-k1*k2*x1*sqrt(k3*x2)/(k1+k2*x1)-k4*k5*x2;
dx2dt=k1*k2*x1*sqrt(k3*x2)/(k1+k2*x1)+k5*x2;

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