In optimum control, what is intended by discrete scaling?

58 Views Asked by At

I have been looking for strategies to solve my optimal control problem as it is severely suffering from scaling issues. I then came across this article (https://arxiv.org/pdf/1810.11073.pdf) and it mentions that rather than scaling the problem at the "discrete level", one should scale at the optimum control level.

It seems a little cryptic at first but my intuition is that by discrete level scaling we mean that all inputs, that is all parameters of the optimum control problem that have units are scaled with respect to scaling factors that we choose. This means that if we have a problem where $\bf{x}$ is our vector of state variables, the starting values to the problem would be

$\tilde{\bf{x}}=\bf{SF} \bigotimes \bf{x}$

where $\bf{SF}$ is our vector of scaling factors.

Is this what the article is referring to as "discrete level" scaling?