Asked by SARNENDU JATI
on 14 Jun 2018

I'm trying to optimise the cost function for a simple pendulum on a cart. I have written the following code that returns the value of J(cost function) fobs2.m

function [J,u_candidate_fnc] =fobs2(lambda) sol=void(lambda(1),lambda(2),lambda(3),lambda(4)); t=0:0.001:4.452; u_candidate_fnc=candidate_fnc(t,lambda); J=(max(sol.y(1,:))-pi)^2+ abs(max(candidate_fnc)) + abs(max(sol.y(3,:)));

Candidate_fnc.m defines candidate function for acceleration of the cart as the input to the system.

function u=candidate_fnc(t,lambda) Tf=4.4520; w=2*pi/Tf; u1=lambda(1)*sin(w*t); u2=lambda(2)*sin(2*w*t); u3=lambda(3)*sin(3*w*t); u4=lambda(4)*sin(4*w*t); u5=(-5*lambda(1) -5/2*lambda(2)-5/3*lambda(3)-5/4*lambda(4))*sin(5*w*t); u=u1+u2+u3+u4+u5;

I used BVP solver to give me better trajectories using initial guesses. I've written the following code to store the new trajectories in sol. void.m:

function y=void(lambda1,lambda2,lambda3,lambda4) lambda=[lambda1 lambda2 lambda3 lambda4]; t_opt=linspace(0,4452*0.001,4452)'; solinit = bvpinit(t_opt,@xinit_fcn,lambda); sol = bvp4c(@system_odeset_fcn,@bc_function,solinit);

% disp('Lambda values: ') y=sol;

when I run fobs2.m it says, not enough input arguments in sol=void(lambda(1),lambda(2),lambda(3),lambda(4)); and Undefined variable "sol".

Answer by Walter Roberson
on 14 Jun 2018

Accepted Answer

I had to get xinit_fcn from your https://www.mathworks.com/matlabcentral/answers/405238-how-to-resolve-interp1-error

I do not get any error about not enough input arguments when I invoke fobs2(lambda) . I do, however, run into problems with interp1 .

Your xinit_fcn is invoking interp1 with an x1_opt value derived from the t value that is passed into the function. However, bvpinit invokes the function with **individual** t values, not with the entire list of t values, so x1_opt will be a scalar. You are then trying to interp1(1 x 4452, 1 x 1, 1 x 1) . That fails because the second parameter must be the same length as the first parameter.

If you *did* have the entire original list of time values passed in, and were calculating x1_opt= -(pi/Tf)*All_t + pi and wanting to interpolate at the *particular* time, t, that was passed in to the xinit_fcn, then the result would always be the same as -(pi/Tf)*t + pi where t is the individual t. So it is not clear why you do not just have your xinit_fcn return -(pi/Tf)*t + pi .

SARNENDU JATI
on 14 Jun 2018

It is the same. I just took off the transpose. I plotted it and I'm getting the required result for x1_opt.

adjusted code:

function xinit = xinit_fcn(t) t_opt=linspace(0,4452*0.001,4453); Tf=4.453; t=0:0.001:4.452; x1_opt= -(pi/Tf)*t + pi; figure,plot(x1_opt) x1_opt= -(pi/Tf)*t + pi; x2_opt=0; x3_opt=0; x4_opt=0; xinit=[interp1(t_opt,x1_opt,t); %x1* interp1(t_opt,x2_opt,t); %x2* interp1(t_opt,x3_opt,t); %x3* interp1(t_opt,x4_opt,t);] ; %x4*

Walter Roberson
on 15 Jun 2018

You have

x2_opt=0; x3_opt=0; x4_opt=0; xinit=[interp1(t_opt,x1_opt,t); %x1* interp1(t_opt,x2_opt,t); %x2* interp1(t_opt,x3_opt,t); %x3* interp1(t_opt,x4_opt,t);] ; %x4*

Your x2_opt, x3_opt, and x4_opt are each scalar 0, not zeros the same size as t_opt. And with them being constant 0, there is little point doing interpolation: just output 0 without interpolation.

x2_opt=0; x3_opt=0; x4_opt=0; xinit=[interp1(t_opt,x1_opt,t); %x1* x2_opt; %x2* x3_opt; %x3* x4_opt;] ; %x4*

SARNENDU JATI
on 15 Jun 2018

Yeah, you're right. Thank you.

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## 3 Comments

## Walter Roberson (view profile)

Direct link to this comment:https://www.mathworks.com/matlabcentral/answers/405625-optimisation-of-cost-function#comment_578629

When you run fobs2, what are you passing to fobs2 on the command line?

## Walter Roberson (view profile)

Direct link to this comment:https://www.mathworks.com/matlabcentral/answers/405625-optimisation-of-cost-function#comment_578795

At one point you had commented

but did you then invoke

or did you just expect fobs2 to find the variable named lambda that you had assigned to?

## SARNENDU JATI (view profile)

Direct link to this comment:https://www.mathworks.com/matlabcentral/answers/405625-optimisation-of-cost-function#comment_578804

I invoked fobs2(lambda)

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