# How to set up fmincon

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sam plant on 13 Dec 2018
Reopened: madhan ravi on 13 Dec 2018
I have an objective function which takes input values for a projectile with initial speed v0 and angle theta. Given a target it then calculates the minimum distance of the trajectory to the target and outputs the minimum distance d.
Of course i need to use fmincon to get the minimum distance of the objective function less than 0.1 so that the projectile hits the target but I'm having trouble understanding how to set fmincon up with inputs.
Any Help would be appreciated!

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sam plant on 13 Dec 2018
It uses ode45
function M=objective(initial,target)
v0=initial(1);
theta=initial(2);
h=0;
dt=0.01;
maxtime=60;
range=solve_ode45(v0,theta,h,dt,maxtime); %calculates projectiles path
compare = [target(1)-range(:,3),target(2)-range(:,4)]; %compares displacement of target to line at all points
d=sqrt(compare(:,1).^2+compare(:,2).^2); %magnitude of displacement to give distance at all points
M=min(d); %finds the minimum distance
madhan ravi on 13 Dec 2018
solve_ode45??
sam plant on 13 Dec 2018
that's another function i had to write using ode45, i have to write 3 functions inside of each other

Torsten on 13 Dec 2018
Edited: Torsten on 13 Dec 2018
function main
v0=...; % start value for initial velocity
theta0=...; % start value for angle
target=[... , ...]; % target position
x0 = [v0, theta0];
x = fminsearch(@(x)objective(x,target),x0)
end
function M=objective(initial,target)
v0=initial(1);
theta=initial(2);
h=0;
dt=0.01;
maxtime=60;
range=solve_ode45(v0,theta,h,dt,maxtime); %calculates projectiles path
compare = [target(1)-range(:,3),target(2)-range(:,4)]; %compares displacement of target to line at all points
d=sqrt(compare(:,1).^2+compare(:,2).^2); %magnitude of displacement to give distance at all points
M=min(d); %finds the minimum distance
end

#### 1 Comment

sam plant on 13 Dec 2018
thank you so much! it's worked!

Alan Weiss on 13 Dec 2018
Take a look at Optimize an ODE in Parallel. You probably need to specify a time at which the projectile hits the closest to the target. In the example, we use fzero to find when the projectile hits the ground, and you will probably have to define a similar stopping criterion and use fzero also. Or maybe use an interpolation of the trajectory to find the minimum distance. You can easily interpolate an ODE45 solution by using deval.
Alan Weiss
MATLAB mathematical toolbox documentation