I am having issues while using fmincon to solve optimization problem

I am having issue regarding the error: Error using fmincon

FMINCON requires all values returned by functions to be of data type double.

Here is my MATLAB code

% Vehicle has to travel 300m and in 20 seconds
% and the maximum speed limit on the road is 100kmph(~27.8 m/s)
% and the maximum acceleration of vehicle is 4m/s^2.
% The range of velocity is (0, 27.7) in m/s
% and the range of acceleration is (-4, 4) in m/s^2
% The vehicle stops at end (300m) and the final velocity is 0 m/s
% and the final acceleration is also 0 m/s^2.
% Find the velocity and the acceleration trajectory throughout the journey 
% so that energy consumption is minimized (∫a*ds or v*dv)

% Define the parameters 

d=300;      % distance to be covered in metres
t_f=20;     % final time in seconds
v_0=20;     % intial velocity in m/s
v_f=0;      % final velocity in m/s
a_0=3;      % intial acceleration in m/s^2
a_f=0;      % final acceleration in m/s^2
a_max=4;    % maximum acceleration in m/s^2
a_min=-4;   % minumum acceleration in m/s^2
v_max=27.7; % maximum velocity in m/s
v_min=0;    % minimum velocity in m/s
dt=0.1;      % time step

% Define arrays for the velocity, acceleration, and distance

t= 0:dt:t_f;
s=zeros(size(t));
v=zeros(size(t));
a=zeros(size(t));
ds=zeros(size(t));

% Define the intial conditions
s(1)=0;
v(1)=v_0;
a(1)=a_0;
ds(1)=0;

% Forming optimization problem

lb = [-4,-0.01];
ub = [4,50];

% Options
myopt = optimoptions('fmincon');
myopt.Display = 'iter';

% Function handle
cost = @(x) costFun(x, a, ds, t_f, dt);
constraint = @(x) constraintFun(s, v, a, v_f, a_f, d);

% Solve
x0=[4,0]; %Intial acceleration and velocity

x = fmincon(cost,x0,[],[],[],[],lb,ub,constraint,myopt);


function E = costFun(x, a, ds, t_f, dt)

% Define arrays for the velocity, and distance

v= zeros(size(a));
s=zeros(size(a));

v(1)=20;  %Intialize the intial velocity
s(1)=0;  %Intialize %the intial displacement



for i=2:((t_f/dt)+1)
    
    %compute the velocity, acceleration  and distance using 1-D equation of motion
    
    a(i-1)=3;
    v(i)=v(i-1)+a(i-1)*dt;
    
    s(i)=s(i-1)+ v(i-1)*dt + (0.5*a(i-1)*dt*dt);
    
    ds(i)=s(i)-s(i-1);
    
    
    
    % Apply the constraints on the velocity and acceleration
    if v(i) > 27.7
        v(i) = 27.7;
    end
    
    if v(i) < 0
        v(i) = 0;
    end
    
    if a(i) > 4
        a(i) = 4;
    end
    
    if a(i) < -4
        a(i) = -4;
    end
    
end


% Create the cost function for energy consumption
E = double(sum(a.*ds));

end

% Create constraint function
function [cInEq,cEq] = constraintFun(s, v, a, v_f, a_f, d)

% A local function for the constraints

% Nonlinear inequality constraint: None
cInEq = [];

% Equality constraint
cEq = [s(end)==d; v(end)==v_f; a(end)==a_f];
end

[Torsten]

I find it strange that neither your cost function nor your constraint function depend on the solution variables. Something must be wrong with your code. I fear: not only something.

Answer 1

[Matt J]

cEq = [s(end)-d; v(end)-v_f; a(end)-a_f];