MATLAB: Fit an Ordinary Differential Equation (ODE) using lsqcurvefit

fit an odelsqcurvefitode45system of ode's

Hello,

i have a system of 11 ODE's (ode45) and want to fit them to measured data. For that i have 11 variables i want to optimate. My Question:

Additional to the lb and ub in the lsqcurvefot solver, i want a condition for the variables like x(1)+x(2)=5. Is that possible?

Best Answer

Remove parameters x(1) and x(2) from your list and introduce one new variable x(12). From x(12), calculate x1=5*cos^2(x(12)) and x2=5*sin^2(x(12)) and insert x1 and x2 instead of x(1) and x(2) in your ODE system.

If your constraints are more complicated than this one, use "fmincon" instead of "lsqcurvefit".

Related Solutions

MATLAB: Maximize a system of nonlinear equation

One approach:

f = @(x) norm([x(1).^2 + 2*x(2) + x(3); exp(x(1)).*sin(x(2)) + cos(x(3))]);
[X, fval] = fminunc(@(x)-f(x), rand(3,1));

Here ‘f’ has 2 equations in 3 unknowns. Use your own equations, and your own constraints with fmincon.

MATLAB: Fit an Ordinary Differential Equation (ODE) using fmincon

function main
% ydata from excel 
filename = 'Messung_1.xlsx';
sheet = 12;
Range1 = 'C6:C3790';
Range2 = 'D6:C3790';
t_Kl = xlsread(filename,sheet,Range1)+273.15;
t_Nl = xlsread(filename,sheet,Range2)+273.15;
ydata = [t_Kl t_Nl];
p0 = ones(1,4);
pbest = fmincon(@(p)objective(p,ydata),p0);
end
function diff = objective(p,ydata)
tspan = linspace(0,3785,3785);
ic = [300 300];
f = @(t,T,p) [(p(1)*(T(2)-T(1))+p(2))/100; p(3)*(T(1)-T(2))+p(4)*(300-T(2))];
[t,T] = ode45(@(t,y)f(t,y,p),tspan,ic);
diff = sum(((T(:,1)-ydata(:,1))./ydata(:,1)).^2)+sum(((T(:,2)-ydata(:,2))./ydata(:,2)).^2);
end

Best Answer

Related Solutions

MATLAB: Maximize a system of nonlinear equation

MATLAB: Fit an Ordinary Differential Equation (ODE) using fmincon

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