Reachability for purely continuous nondeterministic LTI systems using zonotopes

JuliaReach / Reachability.jl

Reachability and Safety of Nondeterministic Dynamical Systems

MIT License

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Reachability for purely continuous nondeterministic LTI systems using zonotopes #385

Closed mforets closed 5 years ago

mforets commented 6 years ago

See:

https://juliareach.github.io/LazySets.jl/latest/man/reach_zonotopes.html#Introduction-1
Reachability of uncertain linear systems using zonotopes. A. Girard, HSCC2015.
Efficient computation of reachable sets of linear time-invariant systems with inputs. A. Girard, C. Le Guernic, O. Maler. HSCC2016.

mforets commented 5 years ago

See this notebook for a recap on the theory and a proof of principle implementation.

mforets commented 5 years ago

The pictures show the flowpipe of a 2x2 system x' = Ax (in the notebook) using (i) the concrete zonotopes reach algorithm, (ii) block decomposition.

Runtime is

252.789 μs (1134 allocations: 95.14 KiB) for (i)
17.015 ms (20801 allocations: 1.24 MiB) for (ii)

mforets commented 5 years ago

This algorithm was added as GLGM06 in #531.