How to compute numerical gradient of an unknown function in matlab Simulink?

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Hi! I have a function that is unknown and that is being generated at every time instant t in my simulink model (Imagine it like a black box, wherein, I have data for at every time instant but not the mapping itself, the data looks something like this: ). In order to implement my algorithm, I need to find the direction that corresponds to greatest decrease (or increase) of this scalar mapping at every time instant. So, how can I find the numerical gradient descent of this unknown function at every time step, i.e at any ? The only thing known is that is lipshitz continuous. Kindly suggest me ways in which it can be implemented in simulink. Thanks for your time and consideration.

Answers (1)

Torsten on 19 Jul 2019
The i'th component gi of the gradient vector g is approximately given by
gi = (f(x1,...,xi+h,...,x10)-f(x1,...,xi,...,x10))/h
Thus for each time t, given (x1,...,x10), you will have to evaluate f at (x1+h,x2,...,x10),(x1,x2+h,x3,...,x10),...,(x1,x2,...,x10+h) and calculate the gi.
Torsten on 22 Jul 2019
Edited: Torsten on 22 Jul 2019
How can you give both u(w) and u(w+h) to the system?
If this is a technical problem that concerns SIMULINK, I can't answer it.
As you wrote, u is the control input specified by you. So in general, it should be possible to evaluate it at (x(t),w(t)) and (x(t),perturbed w(t)).

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