Minimize φ using mathematical optimization toolbox

x(t) is a matrix which is a function of t, of order Nx2

The final equation is required in be variable form (variables- φ, n, N, x, t0, tf) here, t0 = initial point on 2D plane (time 0 sec.) tf= final point on 2D plane (time when robot reaches the goal point, x(tf) ) please note that the x(t) is in differential form in the equation mentioned above.

[Alan Weiss]

If this is a homework problem, please let us know what you have tried already.

If this is not homework, then please let us know what kind of advice you are looking for.

Alan Weiss

MATLAB mathematical toolbox documentation

[Vanshika Singh]

This isn't any homework.

I know how to perform integral and matrix multiplication. but I need to solve to the following equation, where I need help to define x(t) matrix which in differential form. steps I have applied- Take x(t) and its differential form. multiply it with its transpose. integral over tf to t0

summation from 0 to N.

need help in step 1&2. I want to minimize this equation and need final equation in form of variables only. I guess we need to use optimization toolbox , fmincon.

[Torsten]

xi_dot(t)=0 for all i minimizes the functional.

Since I don't think that this solution is what you are asking for, my guess is that there are some constraints on the xi that you didn't mention.

[Vanshika Singh]

Sorry for not mentioning the constraints.

these are the equations-

Answer 1

[Erik Keever]

Since you say you can evaluate the functional,

zeta = functional(x_i(t); phi, gamma)

It sounds like all you need to do is make an anonymous handle to evaluate it given the phi/gamma parameters and pass that to one of the optimization toolbox's blackbox minimizers, which will in turn look for gamma and phi that minimizes zeta.

Since you haven't stated any constraints I might suggest to use fminunc rather than fmincon, but it's not exactly clear what the question is: Are we actually seeking x_i(t) (i.e. solving the functional calculus extremization problem numerically), or phi, or both simultaneously?

[Vanshika Singh]

I have listed the constraints above, please help. we are not much concerned with phi. We are looking for minimizing gamma

[Vanshika Singh]

We wish to minimize phi , which is a function of x(t)_dot and its transpose.