A Summary of Recent Progress on Efficient Parametric Approximations of Viability and Discriminating Kernels

9 pages•Published: December 18, 2015

Abstract

Viability and discriminating kernels are powerful constructs for analyzing system safety through model checking, but until recently the only computational algorithms available were nonparametric grid-based approaches which, although accurate, scaled exponentially with the dimension of the system's state space. In contrast, several polynomial complexity reachability algorithms have been developed using various parametric set representations. In a recent series of papers, two of these parametric approaches -- based on ellipsoids and support vectors -- have been adapted to approximate viability and discriminating kernels in the discrete, continuous and sampled data models of time. This paper briefly summarizes these algorithms and compares their key features with one another and with a representative nonparametric approach.

Keyphrases: ellipsoidal representation, reachability analysis, support function representation, viability theory

In: Sergiy Bogomolov and Ashish Tiwari (editors). Symbolic and Numerical Methods for Reachability Analysis, 1st International Workshop, SNR 2015, vol 37, pages 23-31.

Links:	https://easychair.org/publications/paper/TZj
	https://doi.org/10.29007/bm16