nonlcon with 2 possible values

I am using fmincon to optimize a space trajectory. My controls are the thrust three directions (radial(Tr), tangential(Tt) and normal(Tn)).

During my trajectory, I want the thrust to be either equal to the maximum possible value (Tmax) available or null. To express this constrain I want to use

sqrt(Tr^2+Tt^2+Tn^2)

ceq=[ or

sqrtT(r^2+Tt^2+Tn^2)-Tmax

How can I express this nonlinear constrain in my script? is it possibile to write the constrain with an or operator?

Answer 1

[Nipun]

Hi Alessia,

I understand that you want to apply a nonlinear constraint to your optimization problem in MATLAB using fmincon, where the thrust can either be zero or the maximum possible value (Tmax). Here's how you can define this constraint:

function [c, ceq] = thrustConstraint(x)
    Tmax = ...; % Define your Tmax value here
    Tr = x(1); % Radial thrust
    Tt = x(2); % Tangential thrust
    Tn = x(3); % Normal thrust

    thrust = sqrt(Tr^2 + Tt^2 + Tn^2);

    % Nonlinear equality constraints
    ceq = [thrust; thrust - Tmax];
    
    % No inequality constraints
    c = [];
end

When using fmincon, specify this function as the nonlinear constraint function.

Hope this helps.

Regards,

Nipun