Hello all, how I can solve ODE simultaneously with fmincon?

I have a system subject to ordinary differential equations (ODE) which are the linear equality constraints and at the same time i want to minimize the objective function which depends on the parameters which are the solution of the (ODE). I try to follow MathWorks Support Team answer

http://www.mathworks.com/matlabcentral/answers/101883-how-do-i-estimate-or-optimize-the-parameters-of-my-ode-system-in-matlab-8-1-r2013a

The problem I have a confuse to follow MathWorks Support Team answer ; I do not know if I have to solve ODE first then I send the ODE solution to the objective function via fmincon as a passing parameters OR I have to solve the ODE inside the objective function. Thanks

[Torsten]

If the ODEs are constraints of your minimization problem, you will have to call the ODE integrator within the "nonlcon" function of fmincon.

Best wishes

Torsten.

[Arjun Manoj]

How do you pass the ode integrator inside nonlcon function?

[Alan Weiss]

For example,

function [c,ceq] = nonlcon(x,extraParams)
ceq = [];
sol = ode45(@odefun,tspan,y0); % You can include tspan or y0 in extraParams
y = deval(sol,extraParams.mytimes); % Assume you want the values at some times
% Figure out the constraint value, for example,
c = y - 25; % You want y to be less than 25
end

You would call this as

nlcon = @(x)nonlcon(x,extraParams);

where extraParams is a structure with the extra parameters, if any, that you want to pass to the nonlinear constraint function.

Alan Weiss

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