Prospective Algorithms

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Marcelo Forets edited this page Oct 3, 2020 · 9 revisions

Linear

Convergent Under-Approximations of Reachable Sets and Tubes for Linear Uncertain Systems. M. Serry. pdf
Reachability Analysis of Large Linear Systems with Uncertain Inputs in the Krylov Subspace. Matthias Althoff. pdf
Wetzlinger, M., Kochdumper, N., & Althoff, M. (2020). Adaptive Parameter Tuning for Reachability Analysis of Linear Systems. arXiv preprint arXiv:2006.12091.
Han, Zhi, and Bruce H. Krogh. "Reachability analysis of large-scale affine systems using low-dimensional polytopes." International Workshop on Hybrid Systems: Computation and Control. Springer, Berlin, Heidelberg, 2006. article

Nonlinear

Incremental affine abstractions for nonlinear systems. Syed M. Hassaan, Mohammad Khajenejad, Spencer Jensen, Qiang Shen and Sze Zheng Yong. https://arxiv.org/pdf/2004.01408.pdf
Thabet, R. E. H., Combastel, C., Raissi, T., Ramdani, N., & Zolghadri, A. (2014, June). Computing reachable sets for nonlinear systems in presence of bounded uncertainties. In 2014 European Control Conference (ECC) (pp. 227-233). IEEE.

Delay DEs

Over- and Under-Approximating Reach Sets for Perturbed Delay Differential Equations. Bai Xue, Qiuye Wang, Shenghua Feng and Naijun Zhan https://arxiv.org/pdf/1812.11718.pdf
Safe Over- and Under-Approximation of Reachable Sets for Delay Differential Equations. https://www.springerprofessional.de/en/safe-over-and-under-approximation-of-reachable-sets-for-delay-di/14961066

Impulsive systems

Safety Verification for Impulsive Systems. Petro Feketa ∗ Sergiy Bogomolov ∗∗ Thomas Meurer ∗

Examples section:

https://github.com/JuliaReach/Reachability.jl/pull/162/files

XFZ18:

https://github.com/JuliaReach/Reachability.jl/pull/502/files https://github.com/JuliaReach/Reachability.jl/issues/449

Parallel:

https://github.com/JuliaReach/Reachability.jl/pull/236

NLN Invariant:

https://github.com/JuliaReach/Reachability.jl/pull/595/files

Using References:

https://github.com/JuliaLang/julia/blob/46ce4d79337bdd257ee2e3d2f4bb1c55ff0a5030/stdlib/LinearAlgebra/src/dense.jl#L1277-L1322

User API:

https://github.com/JuliaIntervals/IntervalOptimisation.jl/issues/24#issuecomment-565145633