Add star set representation

[mforets]

Proposal: add the symbolic set representation of generalized stars.

This set representation has applications in reachability analysis [1].

References:

• Duggirala, P. S., & Viswanathan, M. 2016, July. Parsimonious, simulation based verification of linear systems. In International Conference on Computer Aided Verification pp. 477-494. Springer, Cham.

[schillic]

Stars are also used in Hylaa.

[mforets]

Ok thanks for the pointer, i thought my ref was the same set of people but it is not, although the intersection is non-empty (HyLAA ref).

[mforets]

Star sets used also in Safety Verification of Cyber-Physical Systems with Reinforcement Learning Control.

Here is a tentative definition:

# it is not generally convex but i make it <: LazySet
struct Star{N<:Real, VN<:AbstractVector{N}} <: LazySet{N}
    c::VN # center
    V::Vector{VN} # basis
    P::HPolyhedron{N} # predicate
end

In particular, the predicate function is implemented as a conjunction of linear constraints.