Algebraic Invariants for Linear Hybrid Automata

TL;DR

This paper presents an algorithm to compute the strongest algebraic invariants for unguarded linear hybrid automata, leveraging a control-theoretic discretisation technique to preserve invariants.

Contribution

It introduces a novel method to determine algebraic invariants in linear hybrid automata using a discretisation approach that maintains the original invariants.

Findings

Algorithm computes strongest algebraic invariants

Discretisation preserves continuous dynamics invariants

Applicable to unguarded linear hybrid automata

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.