# Time varying input in ReachabilityAnalysis

Let’s take the following example taken from ReachabilityAnalysis's documentation: Transmision line · ReachabilityAnalysis.jl

For the input, it takes the following assumption

We are interested in the step response to an input voltage Uin(t), constant for t \in [0, T] over the domain U_{in} = [0.99, 1.01].

Uin = Interval(0.99, 1.01)


What if we are interested in a timevarying input trajectory Uin(t) with an uncertainty interval.

Hi Martin, although the application is not related, I think this artícle (published in Computers & Structures journal less than three months ago) might be helpful to see how time-varying inputs can be introduced in RA systems. However, probably @mforets has comments on your application of interest in particular.

What if we are interested in a timevarying input trajectory

The text in the example has been updated (and refactored under “Modeling uncertain inputs”).

In particular, u ∈ Uin is used for arbitrarily time-varying inputs with bounded range. For less general input models the usual approach is to append extra (dynamic) constraints to the system; examples can be found in the article linked by @jorgepz.