Unable to meet integration tolerances in fmincon to solve ODE optimization problem

[poster]

<p>I have constrained ODE optimization problem to be solved using Matlab, I started by solving the ODE using <code>ode15s</code> which working will this initial values, also I had very good results without constraints using <code>fminsearch</code>, the problem started when I used <code>fmincon</code> it gave me these warnings:</p>

<pre><code>Warning: Length of lower bounds is < length(x); filling in missing lower bounds with -Inf.
> In checkbounds (line 33)
In fmincon (line 318)
In Optimization (line 64)
Warning: Length of upper bounds is < length(x); filling in missing upper bounds with +Inf.
> In checkbounds (line 47)
In fmincon (line 318)
In Optimization (line 64)
Warning: Failure at t=2.340250e+01. Unable to meet integration tolerances without reducing the step size below the smallest value
allowed (5.684342e-14) at time t.
> In ode15s (line 668)
In ObjFun (line 6)
In barrier
In fmincon (line 813)
In Optimization (line 64)
</code></pre>

<p>I tried to remove constraints, but nothing changed...</p>

<pre class="lang-matlab prettyprint-override"><code>y1_max = 5; y2_max = 2.3;
y01 = 1; y02 = 1.6;

%Control function parameter
Umin = -0.3; Umax = -0.1;

%Creation the structure of model parameters
params.T0=T0; params.Tf=Tf;
params.y1d=y1d; params.y2d=y2d;
params.y01=y01; params.y02=y02;
params.y2_max=y2_max;

n=2;
U0=-0.2*ones(1,n);
params.n=n;
params.U=U0; params.Umax=Umax; params.Umin=Umin;
params.dt=(Tf-T0)/n;

%for initial value of optimization parameters
options = odeset('RelTol',1e-7,'AbsTol',1e-7);
U=U0;

[t,y]=ode15s(@ODEsolver,[T0,Tf],[y01 y02],options,params);

%adding the ode solution as input prameters
params.t=t; params.y1= y(:,1); params.y2= y(:,2);

U0=-0.2*ones(1,n);
params.n=n; params.U=U0;
params.dt=(Tf-T0)/n;

A = [];
B = [];
Aq = []; Bq = [];
options1 = optimset('MaxIter',5000);
[x,fval,exitflag,output] = fmincon(@ObjFun,U0,A,B,Aq,Bq,Umin,Umax,IneqConst(U0,params),options1,params)
</code></pre>

<pre class="lang-matlab prettyprint-override"><code>function y = ODEsolver(t,y,params)
dt = params.dt;
nu = floor(t/dt)+1;
nu = min(nu,params.n-1);

t1 = (nu-1)*dt;
Ut = params.U(nu) + ((t-t1)/dt)*(params.U(nu+1) - params.U(nu));

dy1a = ((0.63*y(1))/(1 + y(1)));
dy1b = (Ut*y(1)*y(2))/(1+0.6*y(1));
dy1 = dy1a + dy1b;

dy2a = (0.15*y(2))/(0.05-0.2*y(2));
dy2 = -0.2*y(2) + dy1b * dy2a;

y = [dy1; dy2];
end
</code></pre>

<pre class="lang-matlab prettyprint-override"><code>function ObjFun1 = ObjFun(u,params)
% Calculating the value of the optimization criteria
params.U=u;

options = odeset('RelTol',1e-8,'AbsTol',1e-8);
[t,y]=ode15s(@ODEsolver,[0,100],[params.y01,
params.y02],options,params);

ObjFun1 =trapz(t,(y(:,1)-params.y1d).^2);
end
</code></pre>

<pre class="lang-matlab prettyprint-override"><code>function [c,Const] = IneqConst(u, params)
params.U=u;
options = odeset('RelTol',1e-8,'AbsTol',1e-8);
[t,y]=ode15s(@ODEsolver,[0,100],[params.y01, params.y02],options,params);

c =[];
yCon = y(:,2)-params.y2_max;
Const = trapz(t,(abs(yCon)+yCon).^2);
end
</code></pre>



More answer... (https://stackoverflow.com/questions/58635597/unable-to-meet-integration-tolerances-in-fmincon-to-solve-ode-optimization-probl)