PHAVer: Algorithmic Verification of Hybrid Systems Past HyTech

Abstract

Abstract. In 1995, HyTech broke new ground as a potentially powerful tool for verifying hybrid systems -yet it has remained severely limited in its applicability to more complex systems. We address the main problems of HyTech with PHAVer, a new tool for the exact verification of safety properties of hybrid systems with piecewise constant bounds on the derivatives. Affine dynamics are handled by on-the-fly overapproximation and by partitioning the state space based on user-definable constraints and the dynamics of the system. PHAVer's exact arithmetic is robust due to the use of the Parma Polyhedra Library, which supports arbitrarily large numbers. To manage the complexity of the polyhedral computations, we propose methods to conservatively limit the number of bits and constraints of polyhedra. Experimental results for a navigation benchmark and a tunnel diode circuit show the effectiveness of the approach.

Automatic Rectangular Refinement of Affine Hybrid Systems

“…5 are encouraging since we were able to verify more efficiently than PHAVer itself the instances NAV01-04, while we used that tool as a black box for analysis of rectangular automata (thus with all heuristics disabled). Also notice that the instance NAV04 was solved by PHAVer after applying heuristic convex hull and bounding box approximations at particular moments of the analysis [7]. Our results are fragile, since another choice of affine functions has lead to computational difficulties, as mentioned above.…”

“…HyTech [9], d/dt [2], PHAVer [7]) use a symbolic analysis of the hybrid automaton with a forward and/or backward approach: starting from the initial (resp. unsafe) states, iterate the operator Post ÂHÃ (resp.…”

“…PPL is a C++ library to manipulate polyhedrons with large rational coefficients and exact arithmetic. We analyze the rectangular system with PHAVer [7], a recent tool for the verification of hybrid systems. This tool is designed to verify affine dynamics hybrid automata, based on forward reachability analysis and user-defined rectangular approximations.…”

Flow* 1.2: More Effective to Play with Hybrid Systems

“…The popular over-approximate representations are convex polytopes [9], ellipsoids [18], zonotopes [14] and support functions [19]. Along with their computation techniques, the tools CheckMate [23], Ellipsoidal Toolbox, PHAVer [11] and SpaceEx [12] are developed. On the other hand, few reachable set representations other than intervals (boxes) [21] are successfully applied to non-linear hybrid systems.…”

Piecewise-Affine Approximations for a Powertrain Control Verification Benchmark

“…SpaceEx handles hybrid systems with affine continuous dynamics and polytopic guards and invariant sets. SpaceEx is based on the PHAver technology, which uses infinite precision representations of polytopic sets to perform the reachable set estimation [3]. SpaceEx incorporates several recent advances in reachable set estimation, such as zonotope [1] representations and support functions [10], which can increase the efficiency and accuracy of the reachable set estimations.…”