Flowpipes

AbstractFlowpipe

Abstract type representing a flowpipe.

Notes

A flowpipe is the set union of an array of reach-sets.

basetype(T::Type{<:AbstractFlowpipe})

Return the base type of the given flowpipe type (i.e., without type parameters).

Input

• T – flowpipe type, used for dispatch

Output

The base type of T.

LazySets.ρ(d::AbstractVector, fp::AbstractFlowpipe)

Input

• d – direction
• fp – flowpipe

Output

The support function of the flowpipe along the given direction d.

Notes

In this fallback implementation, the flowpipe behaves like the union of the reach-sets, i.e. the implementation is analogue to that of a LazySet.UnionSetArray.

LazySets.σ(d::AbstractVector, fp::AbstractFlowpipe)

Input

• d – direction
• fp – flowpipe

Output

The support vector of the flowpipe along the given direction d.

Notes

In this fallback implementation, the flowpipe behaves like the union of the reach-sets, i.e. the implementation is analogue to that of a LazySet.UnionSetArray.

LazySets.dim(fp::AbstractFlowpipe)

Input

• fp – flowpipe

Output

An integer representing the ambient dimension of the flowpipe.

set(fp::AbstractFlowpipe, ind::Integer)

Return the geometric set represented by this flowpipe at the given index.

Input

• fp – flowpipe
• ind – index (from 1 to length(flowpipe))

Output

The set wrapped by the flowpipe at the given index.

set(fp::AbstractFlowpipe, ind::AbstractVector)

Return the union of set represented by this flowpipe at the given indices.

Input

• fp – flowpipe
• ind – vector of indices

Output

The set union stored in the flowpipe at the given indices.

set(fp::AbstractFlowpipe)

Return the geometric set represented by this flowpipe as the union of reach-sets.

Input

• fp – flowpipe

Output

The set union of the array of reach-sets of the flowpipe.

Notes

To retrieve the array of sets stored in the flowpipe use array(fp). To get a set at a particular index, use set(F[ind]) or set(F, ind).

tstart(fp::AbstractFlowpipe)

Return the initial time of this flowpipe.

Input

• fp – flowpipe

Output

A float representing the initial time of the given flowpipe. The fallback is computed by taking the initial time of the first reach-set.

tend(fp::AbstractFlowpipe)

Return the final time of this flowpipe.

Input

• fp – flowpipe

Output

A float representing the initial time of the given flowpipe. The fallback is computed by taking the final time of the last reach-set.

tspan(fp::AbstractFlowpipe)

Return time span of this flowpipe.

Input

• fp – flowpipe

Output

The interval representing the time span of the given flowpipe. The fallback is computed as (tstart(fp), tend(fp)), see tstart(::AbstractFlowpipe) and tend(::AbstractFlowpipe) for details.

vars(fp::AbstractFlowpipe)

Return the tuple of variable indices of the flowpipe.

Input

• fp – flowpipe

Output

Tuple of integers with the variable indices of the flowpipe, typically $1, 2, …, n$ where $n$ is the dimension of the flowpipe.

Notes

The fallback implementation assumes first reach-set is representative.

Flowpipe{N, RT<:AbstractReachSet{N}, VRT<:AbstractVector{RT}} <: AbstractFlowpipe

Type that wraps a flowpipe, which is an iterable collection of reach-sets that behaves like their set union.

Fields

• Xk – array of reach-sets
• ext – extension dictionary; field used by extensions

Notes

The dimension of the flowpipe corresponds to the dimension of the underlying reach-sets; in this type, it is is assumed that the dimension is the same for the different reach-sets.

location(F::Flowpipe)

Return the location of a flowpipe within a hybrid system, or missing if it is not defined.

Input

• F – flowpipe

Output

The :loc_id value of stored in the flowpipe's extension field.

shift(R::AbstractReachSet, t0::Number)

Perform a time-shift of the given reach-set.

Input

• R – reach-set
• t0 – number that corresponds to the time-shift

Output

A new reach-set of the same type of R such that its time-span has been shifted by t0.

shift(fp::Flowpipe{N, <:AbstractReachSet}, t0::Number) where {N}

Return the time-shifted flowpipe by the given number.

Input

• fp – flowpipe
• t0 – time shift

Output

A new flowpipe such that the time-span of each constituent reach-set has been shifted by t0.

HybridFlowpipe{N, D, FT<:AbstractFlowpipe, VOA<:VectorOfArray{N, D, Vector{FT}}} <: AbstractFlowpipe

Type that wraps a vector of flowpipes of the same type, such that they are contiguous in time.

Fields

• Fk – vector of flowpipes
• ext – (optional, default: empty) dictionary for extensions

Notes

The evaluation functions (in time) for this type do not assume that the flowpipes are contiguous in time. That is, the final time of the i-th flowpipe does not match the start time of the i+1-th flowpipe.

MixedFlowpipe{N, D, FT<:AbstractFlowpipe, VOA<:VectorOfArray{N, D, Vector{FT}}} <: AbstractFlowpipe

Type that wraps a vector of flowpipes of the same time, such that they are not necessarily contiguous in time.

Fields

• Fk – vector of flowpipes
• ext – (optional, default: empty) dictionary for extensions

Notes

This type does not assume that the flowpipes are contiguous in time.

ShiftedFlowpipe{FT<:AbstractFlowpipe, NT<:Number} <: AbstractFlowpipe

Type that lazily represents a flowpipe that has been shifted in time.

Fields

• F – original flowpipe
• t0 – time shift

Notes

This type can wrap any concrete subtype of AbstractFlowpipe, and the extra field t0 is such that the time spans of each reach-set in F are shifted by the amount t0 (which should be a subtype of Number).

PartitionedFlowpipe{N, D, FT<:AbstractFlowpipe, VOA<:VectorOfArray{N, D, Vector{FT}}} <: AbstractFlowpipe

Type that wraps a vector of flowpipes of possibly different types.

Fields

• Fk – vector of flowpipes
• ext – (optional, default: empty) dictionary for extensions

Notes

MappedFlowpipe{FT<:AbstractFlowpipe, ST} <: AbstractFlowpipe

Fields

• F – flowpipe
• func – function representing the map