INT{N, AM} <: AbstractContinuousPost

Implementation of a reachability method for linear one-dimensional systems interval arithmetic.

Fields

• δ – step-size of the discretization
• approx_model – (optional, default: Forward) approximation model; see Notes below for possible options

Notes

The type fields are:

• N – number type of the step-size
• AM – approximation model

The default approximation model used in this algorithm is:

Forward(sih=:concrete, exp=:base, setops=:Interval)

In particular, the setops=:Interval flag specifies that intermediate computations in the discretization are done using interval arithmetic. This allows for some optimizations.

References

This algorithm is essentially a non-decomposed version of the method in Bogomolov et al. [BFF+18], using intervals as set representation. For a general introduction we refer to the dissertation [LG09].

Regarding the approximation model, by default we use an adaptation of the method presented in Frehse et al. [FLD+11].

Interval arithmetic operations are performed using the IntervalArithmetic.jl package. Hence, the results are guaranteed to comply to the IEE754 standard with respect to the floating-point operations using intervals.