`ReachabilityAnalysis.TMJets`

— Type`TMJets`

The algorithm TMJets defaults to `TMJets21b`

.

`ReachabilityAnalysis.TMJets21a`

— Type`TMJets21a{N, DM<:AbstractDisjointnessMethod} <: AbstractContinuousPost`

Validated integration using Taylor models with the `validated_integ`

algorithm.

**Fields**

`orderQ`

– (optional, default:`2`

) order of the Taylor models for jet transport variables`orderT`

– (optional, default:`8`

) order of the Taylor model in time`abstol`

– (optional, default:`1e-10`

) absolute tolerance`maxsteps`

– (optional, default:`2000`

) maximum number of steps in the validated integration $x' = f(x)$`adaptive`

– (optional, default:`true`

) if`true`

, try decreasing the absolute tolerance each time step validation fails, until`min_abs_tol`

is reached`minabstol`

– (optional, default:`1e-29`

) minimum absolute tolerance for the adaptive algorithm`disjointness`

– (optional, default:`ZonotopeEnclosure()`

) defines the method to perform the disjointness check between the taylor model flowpipe and the invariant

**Notes**

The argument `disjointness`

allows to control how are disjointness checks computed, in the case where the invariant is not universal. In particular, `ZonotopeEnclosure()`

pre-processes the taylor model with a zonotopic overapproximation, then performs the disjointness check with that zonotope and the invariant. For other options, see the documentation of `AbstractDisjointnessMethod`

.

This algorithm is an adaptation of the implementation in `TaylorModels.jl`

(see copyright license in the file `reach.jl`

of the current folder). The package `TaylorIntegration.jl`

is used for jet-transport of ODEs using the Taylor method, and `TaylorSeries.jl`

is used to work with truncated Taylor series.

`ReachabilityAnalysis.TMJets21b`

— Type`TMJets21b{N, DM<:AbstractDisjointnessMethod} <: AbstractContinuousPost`

Validated integration using Taylor models with the `validated_integ2`

algorithm.

**Fields**

`orderQ`

– (optional, default:`2`

) order of the Taylor models for jet transport variables`orderT`

– (optional, default:`8`

) order of the Taylor model in time`abstol`

– (optional, default:`1e-10`

) absolute tolerance`maxsteps`

– (optional, default:`2000`

) maximum number of steps in the validated integration $x' = f(x)$`adaptive`

– (optional, default:`true`

) if`true`

, try decreasing the absolute tolerance each time step validation fails, until`min_abs_tol`

is reached`minabstol`

– (optional, default:`1e-29`

) minimum absolute tolerance for the adaptive algorithm`disjointness`

– (optional, default:`ZonotopeEnclosure()`

) defines the method to perform the disjointness check between the taylor model flowpipe and the invariant

**Notes**

The argument `disjointness`

allows to control how are disjointness checks computed, in the case where the invariant is not universal. In particular, `ZonotopeEnclosure()`

pre-processes the taylor model with a zonotopic overapproximation, then performs the disjointness check with that zonotope and the invariant. For other options, see the documentation of `AbstractDisjointnessMethod`

.

This algorithm is an adaptation of the implementation in `TaylorModels.jl`

(see copyright license in the file `reach.jl`

of the current folder). The package `TaylorIntegration.jl`

is used for jet-transport of ODEs using the Taylor method, and `TaylorSeries.jl`

is used to work with truncated Taylor series.