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Numerical tools for constraints solving are a cornerstone to controlverification problems. This is evident by the plethora of research that usestools like linear and convex programming for the design of control systems.Nevertheless, the capability of linear and convex programming is limited and isnot adequate to reason about general nonlinear polynomials constraints thatarise naturally in the design of nonlinear systems. This limitation calls fornew solvers that are capable of utilizing the power of linear and convexprogramming to reason about general multivariate polynomials. In this paper, wepropose PolyAR, a highly parallelizable solver for polynomial inequalityconstraints. PolyAR provides several key contributions. First, it uses convexrelaxations of the problem to accelerate the process of finding a solution tothe set of the non-convex multivariate polynomials. Second, it utilizes aniterative convex abstraction refinement process which aims to prune the searchspace and identify regions for which the convex relaxation fails to solve theproblem. Third, it allows for a highly parallelizable usage of off-the-shelfsolvers to analyze the regions in which the convex relaxation failed to providesolutions. We compared the scalability of PolyAR against Z3 8.9 and Yices 2.6on control designing problems. Finally, we demonstrate the performance ofPolyAR on designing switching signals for continuous-time linear switchingsystems.

PolyAR: A Highly Parallelizable Solver For Polynomial Inequality Constraints Using Convex Abstraction Refinement