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.

Fields

• 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

Notes

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 Althoff et al. [ASB07]. For technicalities on interval matrix operations, we refer to the package IntervalMatrices.jl.

References

The main ideas behind this algorithm can be found in Althoff et al. [ASB07]. These methods are discussed at length in the dissertation [Alt10].

Regarding the zonotope order reduction methods, we refer to Combastel [Com03] and Girard [Gir05] and the review article [YS18].