Minimize φ using mathematical optimization toolbox

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Vanshika Singh 2018-10-24

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评论： Vanshika Singh 2018-11-4

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.

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Torsten 2018-10-25

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 2018-10-25

Sorry for not mentioning the constraints.

these are the equations-

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回答（1 个）

Erik Keever 2018-10-25

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在 MATLAB Online 中打开

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?