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-Gr\"{o}bner algorithm to systematically obtain algebraic invariants of polynomial dynamical systems without using Gr\"{o}bner bases or quantifier elimination. We identify totally real varieties as an important class for efficient invariance checking.