Optimization of ODE parameters

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Murad Nazari 2018-3-13

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/387904-optimization-of-ode-parameters

评论： Torsten 2018-3-13

I have a set of data experimental data and want to solve a differential equation with two unknown variable. Those two unknown variable should be tuned that the solution of ode will match the experimental data.I have written the following code but I couldn't move forward. Any help will be appreciated.

Thanks in advance.

load data.mat
expTime = Data (1:6,1);
Tr = Data (1:6,2);
tSpan = [0 10]; 
T0 = Data(1,2); 
x = [10522;53555];
myfun = @(t,T) (5.4675e-4)*exp(-(x(1))/(8.314*T))*(x(2));
T = ode45 (myfun,tSpan,T0); 
simY = deval(T, expTime); 
A = [ 1 , 0];
b =1;
ab0  = [1 ;1];
x = lsqnonlin(@ObjFnc,ab0,0,15000)

In the following code I tried to write an objective function that takes input of two unknown variables, solves ODE, and calculates the error. I couldn't find a way how to calculate the error.

   function cost = ObjFnc(a,b)
    tSpan = [0 10];
    load data.mat
    T0 = Data(1,2);
    expTime = Data (1:6,1);
    myfun = @(t,T) (5.4675e-4)*exp(-a/(8.314*T))*b;
    T = ode45 (myfun,tSpan,T0);
    Tp = deval(T,expTime);
    end