Nonlinear constraint on optimization using ODE - system state involved

2 views (last 30 days)
I need to incorporate a nonlinear constraint on my optimization problem but there is a ODE involved. The constraint involves a system state so that is why I am having some difficulty in incorporating it. I do not know if it can be done.
It is easy to write some constraint that depends only on the paramaters themselves or values that are available at t = 0 (e.g., initial conditions) but I do not know a priori the values of the states. So, adapting one MATLAB example from let us say I am trying to optimize the two parameters in the vector p inside that ODE but some some reason I want to limit y(2) to a maximum value during optimization. Can someone help on this generic example?
tspan = [0 5];
y0 = [0 0.01];
function SSE = fobj(p,tspan,y0)
[t,y] = ode23s(@(t,y) odefcn(t,y,p), tspan, y0);
SSE = sum((y - yexp).^2); % let us say we have some experimental data to define a sum of squared errors
function dydt = ode_example(t,y,p)
dydt = zeros(2,1);
dydt(1) = y(2);
dydt(2) = p(1)*t.*y(1)+p(2);
function [c] = nlincon(y,p,max_value)
c = y(2)-max_value; % ?? how do I access the value of y(2) at all times outside the ODE function itself?

Accepted Answer

Torsten on 9 Aug 2022
I guess you have a time vector for which you have your data vector of measurements "yexp" ?
In nlincon, with these measurement times as tspan and with the actual parameter vector p, call the ODE function and define the vector c of size tspan as
c = y(:,2) - max_value
So defining tspan as [0 5] is not suitable. tspan should exactly contain the times at which "yexp" was measured.

Sign in to comment.

More Answers (0)




Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!