Bounded Verification with On-the-Fly Discrepancy Computation

Fan, Chuchu; Mitra, Sayan

Permalink

https://hdl.handle.net/2142/90444 Copy

Description

Title

Bounded Verification with On-the-Fly Discrepancy Computation

Author(s)

• Fan, Chuchu
• Mitra, Sayan

Issue Date

2015-02

Keyword(s)

• Formal verification
• Hybrid systems
• Reachability
• Algorithms

Abstract

Simulation-based verification algorithms can provide formal safety guarantees for nonlinear and hybrid systems. The previous algorithms rely on user-provided model annotations called “discrepancy functions,” which are crucial for computing reachtubes from simulations. In this report, we eliminate that requirement by presenting an algorithm for computing piece-wise exponential discrepancy functions. The algorithm relies on computing local convergence or divergence rates of trajectories along a simulation using a coarse over-approximation of the reach set and bounding the maximal eigenvalue of the Jacobian over this over-approximation. The resulting discrepancy function preserves the soundness and the relative completeness of the verification algorithm. We also provide a coordinate transformation method to improve the local estimates for the convergence or divergence rates in practical examples. We extend the method to get the input-to-state discrepancy of nonlinear dynamical systems which can be used for compositional analysis. Our experiments show that the approach is effective in terms of running time for several benchmark problems, scales reasonably to larger dimensional systems, and compares favorably with respect to available tools for nonlinear models.

Publisher

Coordinated Science Laboratory, University of Illinois at Urbana-Champaign

Series/Report Name or Number

Coordinated Science Laboratory Report no. UILU-ENG-15-2201

Type of Resource

text

Language

en

Permalink

http://hdl.handle.net/2142/90444

Sponsor(s)/Grant Number(s)

National Science Foundation (CAR 1054247 and NSF CSR 1016791); Air Force Office of Scientific Research (AFOSR YIP FA9550-12-1-0336)

Owning Collections