Underapproximating reach sets

[mforets]

Reachability with underapproximation instead of overapproximation.

Linear:

• https://tel.archives-ouvertes.fr/tel-00422569v1/document
• http://ljk.imag.fr/membres/Antoine.Girard/Publications/hscc2006a.pdf
• https://arxiv.org/pdf/2002.04086.pdf

Nonlinear:

• https://www.cs.utexas.edu/users/hunt/FMCAD/FMCAD14/proceedings/14_chen.pdf
• https://www.sts.tuhh.de/pw-and-m-theses/2017/kitzing17.pdf

[schillic]

• Nonlinear: http://lcs.ios.ac.cn/~znj/papers/HSCC2018b.pdf (If I remember correctly, the approach can also be used to obtain an overapproximation.)

• Generalization to systems with inputs: Inner-Approximating Reachable Sets for Polynomial Systems with Time-Varying Uncertainties

• Taylor models: https://www.cs.colorado.edu/~xich8622/papers/fmcad14.pdf

• Inner and outer approximating flowpipes for delay differential equations

• Inner and outer reachability for the verification of control systems

• Robust under-approximations and application to reachability of non-linear control systems with disturbances (presentation)