fmincon, nonlcon, ode45 - objective output in nonlinear constraint

I want to use the output of the objective function in the nonlinear constraint function. My goal is to constrain a solution of an ODE to a specific max value. The Problem with my code is, that I cant seem to pass over the vectors "init_conds_odes" and "tspan_ode" from the objective function (objective) to the nonlinear constraint function (nonlcontest). Those to vectors are not showing up in the workspace of "nonlcontest" if i set a breakpoint as shown in the code. Is the thing I am trying even possible?

Here is the code:

x_0 = init_vars();
init_conds_odes = [1 5 1 1];

lb = x_0 - 0.1;
ub = x_0 + 43;

options = [];

nlcon = @(H,X,tspan_ode,init_conds_odes) nonlcontest(H,X);
[H] = fmincon(@objective,x_0,[],[],[],[],lb,ub,nlcon,options,init_conds_odes);

function [x_0,tmax] = init_vars()
m = 2;
n = 3;
o = 4;
tmin = 0;
tmax = 5;

x_0 = [m;n;o;tmin;tmax];
end

function [obj_val,X,tspan_ode,init_conds_odes] = objective(H,init_conds_odes)
tmin = H(4);
tmax = H(5);
tspan_ode = [tmin tmax];

[t,X] = ode45(@(t,x) ODEs(t,x,H),tspan_ode,init_conds_odes);

dXdt = zeros(length(t),4);
for i = 1:length(t)
[X(i,:),dXdt(i,:)] = ODEs(t,X(i,:),H);
end

z = max(abs(dXdt(:,2)));

obj_val = z;

end
   
function [X,dXdt] = ODEs(~,X,H)

m = H(1);
n = H(2);
o = H(3);

dXdt = [X(2);
       X(1)/m+X(3)/n+9;
       X(4);
       X(3)/o];
end

function [c,ceq] = nonlcontest(H,~,tspan_ode,init_conds_odes)

% breakpoint here to look at the workspace of nonlcontest. tspan_ode and init_conds_odes are not showing up.
[t,X] = ode45(@(t,x) ODEs(t,x,H),tspan_ode,init_conds_odes);

dXdt = zeros(length(t),4);
for i = 1:length(t)
[X(i,:),dXdt(i,:)] = ODEs(t,X(i,:),H);
end

c = [];
ceq(1) = 0 - X(end,2);
end

Answer 1

[Matt J]

You need to get familiar with Passing Extra Parameters - MATLAB & Simulink. Also, fmincon is not appropriate for the max-norm objective. You need to use fminimax instead:

nlcon = @(H) nonlcontest(H,[],tspan_ode,init_conds_odes);
objfun = @(H) objective(H,init_conds_odes);

options = optimoptions('fminimax','AbsoluteMaxObjectiveCount',length(t));

[H] = fminimax(objfun,x_0,[],[],[],[],lb,ub,nlcon,options);


function [obj_val,X,tspan_ode,init_conds_odes] = objective(H,init_conds_odes)

    tmin = H(4);
    tmax = H(5);
    tspan_ode = [tmin tmax];
    [t,X] = ode45(@(t,x) ODEs(t,x,H),tspan_ode,init_conds_odes);
    dXdt = zeros(length(t),4);
    for i = 1:length(t)
    [X(i,:),dXdt(i,:)] = ODEs(t,X(i,:),H);
    end
    
    
    objval = dXdt(:,2); %<----- minimize the max-norm of this
    
end

[e_frog]

Thanks for the fast answer. If I try it like you suggested I get the following error message, because t is unknown:

Unrecognized function or variable 't'.

Error in test3 (line 13)
options =
optimoptions('fminimax','AbsoluteMaxObjectiveCount',length(t));

And if I comment out the options I get this one:

Unrecognized function or variable 'tspan_ode'.

Error in test3>@(H)nonlcontest(H,[],tspan_ode,init_conds_odes) (line 11)
nlcon = @(H) nonlcontest(H,[],tspan_ode,init_conds_odes);

Error in goalcon (line 104)
                [ctmp,ceqtmp] = feval(confcn{3},x,varargin{:});

Error in fminimax (line 404)
        [ctmp,ceqtmp] = feval(cfun{3},xnew,extravarargin{:});

Error in test3 (line 14)
[H] = fminimax(objfun,x_0,[],[],[],[],lb,ub,nlcon,[]);

Caused by:
    Failure in initial nonlinear constraint function evaluation.
    Optimization cannot continue.

[Matt J]

Well, the first one is easy. Just replace length(t) by whatever the number of time points is going to be. As for the second one, you should probably redo the constraints as,

nlcon = @(H) nonlcontest(H,init_conds_odes);
objfun = @(H) objective(H,init_conds_odes);

function [c,ceq] = nonlcon(H,init_conds_odes)

    tmin = H(4);
    tmax = H(5);
    tspan_ode = [tmin tmax];
    [t,X] = ode45(@(t,x) ODEs(t,x,H),tspan_ode,init_conds_odes);
    dXdt = zeros(length(t),4);
    
    for i = 1:length(t)
    [X(i,:),dXdt(i,:)] = ODEs(t,X(i,:),H);
    end
    
  c = [];
  ceq(1) = 0 - X(end,2);

end

[Matt J]

You should also make sure you are familiar with the material here:

https://www.mathworks.com/help/optim/ug/optimizing-a-simulation-or-ordinary-differential-equation.html

[e_frog]

thanks for the great advice!

[Matt J]

Also relevant:

https://www.mathworks.com/help/optim/ug/objective-and-nonlinear-constraints-in-the-same-function.html