ASB07{N, AM, RM, S, R} <: AbstractContinuousPost

Implementation of Althoff - Stursberg - Buss algorithm for reachability of linear systems with uncertain parameters and inputs using zonotopes.


  • δ – step-size of the discretization
  • approx_model – (optional, default: CorrectionHull(; order=10, exp=:interval)) approximation model; see Notes below for possible options
  • max_order – (optional, default: 5) maximum zonotope order
  • reduction_method – (optional, default: GIR05()) zonotope order reduction method used
  • static – (optional, default: false) if true, convert the problem data to statically sized arrays
  • recursive – (optional default: true) if true, use the implementation that recursively computes each reach-set; otherwise, use the implementation that unwraps the sequence until the initial set


The type fields are:

  • N – number type of the step-size
  • AM – type of the approximation model
  • RM – type associated to the reduction method
  • S – value type associated to the static option
  • R – value type associated to the recursive option

The sole parameter which doesn't have a default value is the step-size, associated to the type parameter N.

The default approximation model is

approx_model=CorrectionHull(order=10, exp=:base)

Here, CorrectionHull refers to an implementation of the interval matrix approximation method described in [ASB07]. For technicalities on interval matrix operations, we refer to the package IntervalMatrices.jl.


The main ideas behind this algorithm can be found in [ASB07]. These methods are discussed at length in the dissertation [ALT10].

Regarding the zonotope order reduction methods, we refer to [COMB03], [GIR05] and the review article [YS18].