Differential Elimination and Algebraic Invariants of Polynomial Dynamical Systems
This work addresses the challenge of verifying safety in cyber-physical systems, which is critical for applications like autonomous vehicles and robotics, but it appears incremental as it adapts existing elimination-theoretic algorithms rather than introducing a fundamentally new paradigm.
The authors tackled the problem of verifying safety properties in cyber-physical systems by developing a method to systematically obtain algebraic invariants for polynomial dynamical systems, using a differential elimination approach without relying on Gröbner bases or quantifier elimination, and they identified totally real varieties to enable efficient invariance checking.
Invariant sets are a key ingredient for verifying safety and other properties of cyber-physical systems that mix discrete and continuous dynamics. We adapt the elimination-theoretic 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.