Differential Elimination and Algebraic Invariants of Polynomial Dynamical Systems

Abstract

Invariant sets are a key ingredient for verifying safety and other properties of cyberphysical systems that mix discrete and continuous dynamics. We adapt the eliminationtheoretic Rosenfeld-Gröbner algorithm to systematically obtain algebraic invariants of polynomial dynamical systems without using Gröbner bases or quantifier elimination. We identify totally real varieties as an important class for efficient invariance checking.