Algebraic Invariants for Linear Hybrid Automata
Logic in Computer Science
2020-11-19 v1 Algebraic Geometry
Abstract
We exhibit an algorithm to compute the strongest algebraic (or polynomial) invariants that hold at each location of a given unguarded linear hybrid automaton (i.e., a hybrid automaton having only unguarded transitions, all of whose assignments are given by affine expressions, and all of whose continuous dynamics are given by linear differential equations). Our main tool is a control-theoretic result of independent interest: given such a linear hybrid automaton, we show how to discretise the continuous dynamics in such a way that the resulting automaton has precisely the same algebraic invariants.
Cite
@article{arxiv.1902.10452,
title = {Algebraic Invariants for Linear Hybrid Automata},
author = {Rupak Majumdar and Joël Ouaknine and Amaury Pouly and James Worrell},
journal= {arXiv preprint arXiv:1902.10452},
year = {2020}
}