GLGM06{N, AM, S, D, NG, P, RM} <: AbstractContinuousPost

Implementation of the Girard–Le Guernic–Maler algorithm for reachability of linear systems using zonotopes.

Fields

• δ – step-size of the discretization
• approx_model – (optional, default: FirstOrderZonotope()) approximation model; see Notes below for possible options
• max_order – (optional, default: 5) maximum zonotope order
• static – (optional, default: false) if true, convert the problem data to statically sized arrays
• dim – (optional default: missing) ambient dimension
• ngens – (optional, default: missing) number of generators
• preallocate – (optional, default: true) if true, use the implementation which preallocates the zonotopes prior to applying the update rule
• reduction_method – (optional, default: GIR05()) zonotope order reduction method used
• disjointness_method – (optional, default: NoEnclosure()) method to check disjointness between the reach-set and the invariant

Notes

The type parameters are:

• N – number type of the step-size
• AM – approximation model
• S – value type of the static option
• D – value type of the dimension of the system dim
• NG – value type of the number of generators ngens
• P – value type of the preallocate option
• RM – type of the reduction method

The only parameter that does not have a default value is the step size δ, associated with the type parameter N. Parameters dim and ngens are optionally specified (default to missing). These parameters are needed for the cases that require the size of the zonotopes to be known (fixed) at compile time, namely the static=true version of this algorithm.

The default approximation model is FirstOrderZonotope.

References

The main ideas behind this algorithm can be found in [GIR05] and [GLGM06]. These methods are discussed at length in the dissertation [LG09].

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