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

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Amardeep Mishra 2019-7-19

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编辑： Torsten 2019-7-22

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.

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回答（1 个）

Torsten 2019-7-19

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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.

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Amardeep Mishra 2019-7-19

Because that would mean that, we'd have to perturb the parameters, and then perturb u and then integrate xdot to find the next state. Now at any given instant of time you can either give u(w). How can you give both u(w) and u(w+h) to the system?