Objective function is undefined at initial point. Fmincon cannot continue.

I am running an optimization using fmincon and I recieved the following error '' Objective function is undefined at initial point. Fmincon cannot continue.''

when the time step DT (which is in bold) is increased from 1 to 2 the code runs without any error but when set to 1, I am getting the error

please find part of the code below

data = xlsread('Power_curve.xlsx');
t = data(:,1);
Pl = data(:,2); 
% Define time step for simulation. 
DT = 1;  % This can be increased to decrease computation time
% Define lower and upper bounds for Fuel Cell
PFC_lb = 0; % Lower bound for PFC
PFC_ub = 10000; % Upper bound for PFC
% Define lower and upper bounds for State of Charge
SOCmin = 0.2;
SOCmax = 0.7;
% Battery and Fuel Cell parameters
VFCoc = 62;  % Fuel cell open circuit voltage in Volts
RFC = 0.06;  % Fuel cell resistance in Ohms
RFCup = 10; % Fuel cell ramp up power in kW (value can be changed as required)
RFCdown = -10; % Fuel cell ramp down power in kW (value can be changed as required)
VBToc = 72; % Battery open circuit voltage in Volts
RBT = 0.06; % Battery resistance in Ohms
CBT = 45; % Capacity of the battery in Ah
PBT_max = 15000;
% Initial SOC of the battery
SOC0 = 0.5; % Initial chosen status of battery
mu = 0.6;
%% We will have three variables:
%   Fuel Power: PFC
%   Battery Power: PBT
%   Battery SOC: SOC
% Construct vectors of lower and upper bounds for fmincon
lb = [PFC_lb;-PBT_max;SOCmin];
ub = [PFC_ub;PBT_max;SOCmax];
Aeq = [1, 1, 0]; % Equality matrix for fmincon. This ensures that PFC + PBT = Pload - refer report
options = optimset('display', 'off'); % Display of the system for each time step is off
n = 1;
for i = 1:DT:length(t)
    ti = i % Display current time
    Pload(n) = Pl(i);
    if i == 1
        SOCold = SOC0;
        PFCold = 0;
        PBTold = 0;
    else
        SOCold = SOC(n-1);
        PFCold = PFC(n-1);
        PBTold = PBT(n-1);
    end
    
    x0 = [3000,5000,SOCold]; % Initial values  
    beq = Pload(n);
    [x,fval,exitflag] = fmincon('Objectivefunction', x0, [], [], Aeq, beq, lb, ub, 'Nonlinearequations', options, VFCoc, RFC, VBToc, RBT, CBT, SOCold, ti, DT, PFCold, RFCup, RFCdown);
    % Saving the results
    PFC(n) = x(1);
    PBT(n) = x(2);
    SOC(n) = x(3);
    %     H(n) = fval; % Hydrogen consumption
    
    n = n +1;
end


%Objective function is 
function f = Objectivefunction(x, VFCoc, RFC, VBToc, RBT, CBT, SOCold,SOC_min, SOC_max,mu, ti, DT, PFCold, PBTold, RFCup, RFCdown)

% Minimize Hydrogen consumption
PFC = x(1);
PBT = x(2);
lambda = (1-2*mu*((SOCold -0.5*(SOC_max-SOC_min))/(SOC_max-SOC_min)));
f = PFC + PBT*lambda;
end

Answer 1

[Walter Roberson]

ti becomes SCO_min and DT becomes SCO_MAX in the function. The function computes max minus min and divides by that. Which is a problem if the min and max are the same.

The first ti is 1. When DT is 1 then those are the same and lead to the division by 0

[aditya deepak]

SOC_min and SOC_max must be 0.2 and 0.7 respectively for the whole for loop. can you tell me how ti becomes SOC_min and DT becomes SOC_max

[Torsten]

Call your objective function with the initial guesses for the parameters before the line

[x,fval,exitflag] = fmincon('Objectivefunction', x0, [], [], Aeq, beq, lb, ub, 'Nonlinearequations', options, VFCoc, RFC, VBToc, RBT, CBT, SOCold, ti, DT, PFCold, RFCup, RFCdown);

in your code to see what it returns.

[aditya deepak]

Thank you for your reply. I have used seperate m files for objective function and the main fmincon script. can I call the objective function for initial condition in the mainscript in this case?

[Torsten]

If "fmincon" can, you can do that, too.

[aditya deepak]

Can you tell me how to call it. I got an error saying unrecognised variable

[Torsten]

In the line

[x,fval,exitflag] = fmincon('Objectivefunction', x0, [], [], Aeq, beq, lb, ub, 'Nonlinearequations', options, VFCoc, RFC, VBToc, RBT, CBT, SOCold, ti, DT, PFCold, RFCup, RFCdown);

you tell fmincon to call your objective function as

f = Objectivefunction(x,VFCoc, RFC, VBToc, RBT, CBT, SOCold, ti, DT, PFCold, RFCup, RFCdown)

but your objective function in the code you posted is

function f = Objectivefunction(x, VFCoc, RFC, VBToc, RBT, CBT, SOCold,SOC_min, SOC_max,mu, ti, DT, PFCold, PBTold, RFCup, RFCdown)

so should be called as

f = Objectivefunction(x, VFCoc, RFC, VBToc, RBT, CBT, SOCold,SOC_min, SOC_max,mu, ti, DT, PFCold, PBTold, RFCup, RFCdown)

I don't know which of the two versions is the correct one.

Further, the additional arguments should be directly included as

[x,fval,exitflag] = fmincon(@(x)Objectivefunction(x,VFCoc, RFC, VBToc, RBT, CBT, SOCold,SOC_min, SOC_max,mu, ti, DT, PFCold, PBTold, RFCup, RFCdown), x0, [], [], Aeq, beq, lb, ub, @(x)Nonlinearequations(x,VFCoc, RFC, VBToc, RBT, CBT, SOCold,SOC_min, SOC_max,mu, ti, DT, PFCold, PBTold, RFCup, RFCdown), options);

[aditya deepak]

Thank you for your help. I was able to resolve the issue