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In order to address the imprecision often introduced by widening operators instatic analysis, policy iteration based on min-computations amounts toconsidering the characterization of reachable value set of a program as aniterative computation of policies, starting from a post-fixpoint. Computingeach policy and the associated invariant relies on a sequence of numericaloptimizations. While the early research efforts relied on linear programming(LP) to address linear properties of linear programs, the current state of theart is still limited to the analysis of linear programs with at most quadraticinvariants, relying on semidefinite programming (SDP) solvers to computepolicies, and LP solvers to refine invariants.  We propose here to extend the class of programs considered through the use ofSums-of-Squares (SOS) based optimization. Our approach enables the preciseanalysis of switched systems with polynomial updates and guards. The analysispresented has been implemented in Matlab and applied on existing programscoming from the system control literature, improving both the range ofanalyzable systems and the precision of previously handled ones.

A Sums-of-Squares Extension of Policy Iterations