fmincon, nonlcon - too many input arguments

Hi i am trying to minimize some output of a system of 2 ODEs that also are bound by a nonlinear constraint. Unfortunately I cant seem to get my syntax for implementing the nonlcon right.

To clarify what I want to achieve with the nonlnear constraint: The last value of X(2) (a velocity) has to be zero.

I know this is a fairly common question on here, but the other questions and answers couldn't solve my problem. This is my specific code:

x_0 = init_vars();
init_conds_odes = [1 0 5 0];
lb = x_0 - 54;
ub = x_0 + 43;
options = [];
nlcon = @nonlcon;
[H] = fmincon(@objective,x_0,[],[],[],[],lb,ub,@nonlcon,options,init_conds_odes);

These are the functions:

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

function [obj_val,X] = objective(H,init_conds_odes)
tmax = H(4);
tspan_ode = [0 tmax];
[~,X] = ode45(@(t,x) ODEs(t,x,H),tspan_ode,init_conds_odes);
z = max(abs(X(:,2)));
obj_val = z;
end

function [dXdt] = ODEs(~,X,H)
m = H(1);
n = H(2);
o = H(3);
dXdt = [X(2);
       X(1)/m+X(3)/n+1;
       X(4);
       X(3)/o];
end

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

This is the error message:

Error using test>nonlcon
Too many input arguments.

Error in fmincon (line 639)
        [ctmp,ceqtmp] = feval(confcn{3},X,varargin{:});

Error in test (line 13)
[H] = fmincon(@objective,x_0,[],[],[],[],lb,ub,@nonlcon,options,init_conds_odes);

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

Answer 1

[Walter Roberson]

nonlcon will be passed t and x. You are not required to make use of t, but it will be passed.

function [c,ceq] = nonlcon(~, X)

[e_frog]

that was fast! thank you!

I have another question concernig this code. I hope it is ok to me to ask here otherwise i will open a new question:

I want to achieve that the last value of X(2) (which is X(end,2)) is 0. But the nonlcon only sees the current set of values and not the whole vector X(tspan_ode,1:4). How can I rewrite my nonlcon?

[Walter Roberson]

You cannot achieve that by using nonlinear constraints.

Consider for example a vibrating spring system, and you need to know what spring constant is needed so that at time 10 the spring's acceleration is instantaneously 0. So you are thinking you could somehow write X(end,2) == 0 as a condition. But nonlcon does not know that it is at the end time -- it can look at the time passed in, but fmincon might be doing a "trial" step of different parameters trying to find ones that work. And in the meantime, the acceleration would be expected to pass through a lot of different values.

Ah, we are both confusing fmincon() and ode45() ; I will need to go back and review what you have written before. But z = max(abs(X(:,2))) has the problem that max() is not differentiable and fmincon() requires that the function be differentiable.

[e_frog]

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

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

options = [];

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

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

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

function [obj_val,X,tspan_ode,init_conds_odes] = objective(H,init_conds_odes)
tmax = H(4);
tspan_ode = [0 tmax];

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

%disp(obj_val)

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)

[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

Thanks for your help so far! I tried to write my nonlcon a little bit different. Can you help me finding out why the nonlcontest does not get enough inputs?

Not enough input arguments.

Error in test>nonlcontest (line 95)
[t,X] = ode45(@(t,x) ODEs(t,x,H),tspan_ode,init_conds_odes);

Error in test>@(H,X,tspan_ode,init_conds_odes)nonlcontest(H,X) (line
13)
[H] =
fmincon(@objective,x_0,[],[],[],[],lb,ub,@(H,X,tspan_ode,init_conds_odes)
nonlcontest(H,X),options,init_conds_odes);

Error in fmincon (line 639)
        [ctmp,ceqtmp] = feval(confcn{3},X,varargin{:});

Error in test (line 13)
[H] =
fmincon(@objective,x_0,[],[],[],[],lb,ub,@(H,X,tspan_ode,init_conds_odes)
nonlcontest(H,X),options,init_conds_odes);

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

[Walter Roberson]

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

don't do that !!

You should try to forget that ode45 or fmincon ever accepted extra parameters for the functions by adding the extra parameters at the end of the command lines.

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

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

[Walter Roberson]

Your entire approach is broken, in my opinion. I think you should be rewriting it as a Boundary Value Problem using the bvp*() functions.

[e_frog]

I cant rewrite it as a boundary value problem, because the initial conditions of the odes [pos(1) vel (1) pos(2) vel(2)] (figuratively) must be met. I tried rewriting my new question from this comment. Perhaps you find the time to help me again. I would really much appreciate it!

Rewritten new question

[Walter Roberson]

If those initial conditions must be met, then specify them as part of the boundaries.

Remember that if needed you can add an extra variable to act as an extra layer of differentiation or an extra layer of integration (as needed) in order to be able to put boundary conditions on derivatives or positions.