Differential Elimination and Algebraic Invariants of Polynomial Dynamical Systems

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.