Solving an algebraic loop / iterative loop in MATLAB

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Thomas Ewald 2020-6-22

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https://ww2.mathworks.cn/matlabcentral/answers/552742-solving-an-algebraic-loop-iterative-loop-in-matlab

评论： Thomas Ewald 2020-6-23

Hello everyone!

I have the following problem: I have an iteration loop, that has to converge to a certain value of a vector x, where during the loop the iteration

is calulated directly from

with a nonlinear function f. At some point

is fulfilled (the "distance" between both vectors is smaller than a predefined tolerance value) and the iterations can stop.

I found, that in Simulink this would be called an "algebraic loop" and that simulink can solve this (i also made use of that in the past). The thing now is, that i have this in a matlab code. For now, this is solved with a self-made variable gain controller and a feedback loop.

I was wondering, if there is some way to solve this with matlab onboard tools. In most cases i think that onboard tools are more reliable and faster than self-coded stuff is. I am looking for something like

x = iterate(@f,x0,opts);

that does this.

Any ideas?

Thanks a lot and best wishes so far

Thomas

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Thomas Ewald 2020-6-23

编辑：Thomas Ewald 2020-6-23

Hello,

and thanks for the answer. The problem, as I see it, is that the vector x in the common optimization or search algorithms is varied by the algorithm itself. In my case, I want to vary the vector on my own, with the function I have. So I have basically two outputs (

and

) at the same time. Common algorithms in matlab only take one objective and work on x for themselves.

But the problem of iterating until something converged is not very uncommon, so I think there must be some sort of algorithm in MATLAB to deal with that problem.

Does anybody know how to solve this?

Best

Thomas

Thomas Ewald 2020-6-23

Hello,

I think I found a possible solution. By using the fminunc function, setting SpecifyObjectiveGradient to true and supplying a user defined function to calculate the gradient, I could solve problem.

Maybe this works and is better than the self-made solution.

Thanks a lot and best wishes

Thomas

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