Is there any Online machine learning algorithm for complex dynamical system

[Former Member]

Hi...I have a complex dynamical system which takes input as x1, x2, x3 and gives output as y1, y2, y3. I don't have any mathematical model of the system. x(k) is the present input to the system and y(k) is the present output of the system. My Objective is to find x1(k+1),x2(k+1),x3(k+1) to maximize y1(k+1) + y2(k+1) + y3(k+1). I can only access the present state(k) and past state(k-1) values. Intuitively y_i(k)=f(x1(k),x2(k),x3(k)) where i=1,2,3 . The system only takes inputs s.t a < x1,x2,x3 < b. Is there any online machine learning algorithm which can be applied to solve this problem?

[thomas_mller13]

First of all, it is not clear, that this minimum exists. If e.g. x_i = y_i and the x_i are defined on whole R, there is no minimum.

If you have a large set of training data you can train a neural network to approximate the function. Applying a hill climber alg. you could find an approximation of a local min. of this function  if one exists.