HybridFluctuat: A Static Analyzer of Numerical Programs within a Continuous Environment

A new static analyzer is described, based on the analyzer Fluctuat. Its goal is to synthetize invariants for hybrid systems, encompassing a continuous environment described by a system of possibly switched ODEs, and an ANSI C program, in interaction with it. The evolution of the continuous environment is over-approximated using a guaranteed integrator that we developped, and special assertions are added to the program that simulate the action of sensors and actuators, making the continuous environment and the program communicate. We demonstrate our approach on an industrial case study, a part of the flight control software of ASTRIUM's Automated Transfer Vehicle (ATV).

[1]  Eric Goubault,et al.  Asserting the Precision of Floating-Point Computations: A Simple Abstract Interpreter , 2002, ESOP.

[2]  Thomas A. Henzinger,et al.  The Algorithmic Analysis of Hybrid Systems , 1995, Theor. Comput. Sci..

[3]  Thomas A. Henzinger,et al.  Hybrid Systems: Computation and Control , 1998, Lecture Notes in Computer Science.

[4]  Patrick Cousot,et al.  Abstract interpretation: a unified lattice model for static analysis of programs by construction or approximation of fixpoints , 1977, POPL.

[5]  Brian Campbell,et al.  Amortised Memory Analysis Using the Depth of Data Structures , 2009, ESOP.

[6]  Goran Frehse,et al.  PHAVer: algorithmic verification of hybrid systems past HyTech , 2005, International Journal on Software Tools for Technology Transfer.

[7]  Patrick Cousot,et al.  Integrating Physical Systems in the Static Analysis of Embedded Control Software , 2005, APLAS.

[8]  Olaf Stursberg,et al.  A Case Study in Tool-Aided Analysis of Discretely Controlled Continuous Systems: The Two Tanks Problem , 1997, Hybrid Systems.

[9]  Eric Goubault,et al.  Static Analysis-Based Validation of Floating-Point Computations , 2003, Numerical Software with Result Verification.

[10]  Matthieu Martel,et al.  Some future challenges in the validation of control systems , 2006 .

[11]  Ansgar Fehnker,et al.  Benchmarks for Hybrid Systems Verification , 2004, HSCC.

[12]  Wolfram Luther,et al.  Numerical Software with Result Verification , 2004, Lecture Notes in Computer Science.

[13]  Kousha Etessami,et al.  Analysis of Recursive Game Graphs Using Data Flow Equations , 2004, VMCAI.

[14]  O. Bouissou,et al.  GRKLib: a Guaranteed Runge Kutta Library , 2006, 12th GAMM - IMACS International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics (SCAN 2006).

[15]  Panos J. Antsaklis,et al.  Hybrid Systems V , 1999, Lecture Notes in Computer Science.

[16]  Radhia Cousot,et al.  Abstract Interpretation of Non-monotone Bi-inductive Semantic Definitions , 2008, VMCAI.

[17]  Matthieu Martel,et al.  Abstract Interpretation of the Physical Inputs of Embedded Programs , 2008, VMCAI.