# Time varying input in ReachabilityAnalysis
**URL:** https://discourse.julialang.org/t/time-varying-input-in-reachabilityanalysis/78419
**Category:** Numerics
**Tags:** reachabilityanalysis
**Created:** [March 24, 2022, 5:14pm UTC](https://discourse.julialang.org/t/time-varying-input-in-reachabilityanalysis/78419 "2022-03-24T17:14:52Z")
**Posts on this page:** 3
**Page:** 1
### Author:  [@martincornejo](https://discourse.julialang.org/u/martincornejo)
#### Post date: [March 24, 2022, 5:14pm UTC](https://discourse.julialang.org/t/time-varying-input-in-reachabilityanalysis/78419/1 "2022-03-24T17:14:52Z")
Let’s take the following example taken from `ReachabilityAnalysis`’s documentation: [https://juliareach.github.io/ReachabilityAnalysis.jl/dev/models/TransmissionLine/#Transmission-line-circuit](https://juliareach.github.io/ReachabilityAnalysis.jl/dev/models/TransmissionLine/#Transmission-line-circuit)
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].
```julia
Uin = Interval(0.99, 1.01)
```
What if we are interested in a timevarying input trajectory Uin(t) with an uncertainty interval.
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### Author:  [@jorgepz](https://discourse.julialang.org/u/jorgepz)
#### Post date: [April 6, 2022, 9:26am UTC](https://discourse.julialang.org/t/time-varying-input-in-reachabilityanalysis/78419/2 "2022-04-06T09:26:57Z")
Hi Martin, although the application is not related, I think [this artícle](https://arxiv.org/pdf/2105.05841.pdf) (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.
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### Author:  [@mforets](https://discourse.julialang.org/u/mforets)
#### Post date: [April 14, 2022, 10:10am UTC](https://discourse.julialang.org/t/time-varying-input-in-reachabilityanalysis/78419/3 "2022-04-14T10:10:09Z")
Hi @martincornejo,
> 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.