are given. Unsafe reachable sets are computed in a game theoretic framework to account for worst case behaviors. Overapproximations of the reachable sets are used as constraints in a convex trajectory optimization program at each time step. We prove the safety property of the optimization program

to solve NMF problems in a recursive way. In order to do that, we introduce a new variant called Nonnegative Matrix Underapproximation (NMU) by adding the upper bound constraint V W ≤ M. Besides enabling a recursive procedure for NMF, these inequalities make NMU particularly well-suited to achieve a sparse

Program analysis using abstract interpretation has been successfully applied in practice to find runtime bugs or prove software correct. Most abstract domains that are used widely rely on convexity for their scalability. However, the ability to express non-convex properties is sometimes required

. Such an analysis relies critically on the use of convex polyhedra to represent sets of states. However, the exponential complexity of the polyhedral operations implies that the performance of the analysis would degrade rapidly with the increasing size of the model and the simulation traces. We propose a new

We make a case for sub-polyhedral scheduling using (Unit-)Two-Variable-Per-Inequality or (U)TVPI Polyhedra. We empirically show that using general convex polyhedra leads to a scalability problem in a widely used polyhedral scheduler. We propose meth-ods in which polyhedral schedulers can beat

Abstract—In a previous paper we showed how the continual reachability set can be numerically computed using efficient max-imal reachability tools. The resulting set is in general arbitrarily shaped and in practice possibly non-convex. Here, we present a fixed-complexity piecewise ellipsoidal under-approximation

In this paper we present and analyze a novel algorithm to synthesize controllers enforcing linear temporal logic speci-fications on discrete-time linear systems. The central step within this approach is the computation of the maximal con-trolled invariant set contained in a possibly non-convex safe

us to derive an underapproxima-tion in the form of linear constraints containing all the integer points ensuring reachability or unavoidability, and all the (non-necessarily inte-ger) convex combinations of these integer points, for general PTA with a bounded parameter domain. Our algorithms