Evaluating Model Checking Approaches to Verify Stability of Control Systems in Simulink

This paper examines the verification of stability, a control requirement, over discrete control systems represented as Simulink diagrams, using different model checking approaches and tools. Model checking comprises the (exhaustive) exploration of a model of a system, to determine if a requirement is satisfied. If that is not the case, examples of the requirement's violation within the system's model are provided, as witnesses. These examples are potentially complementary to previous work on automatic theorem proving, when a system is not proven to be stable, but no proof of instability can be provided. We experimentally evaluated the suitability of four model checking approaches to verify stability on a set of benchmarks including linear and nonlinear, controlled and uncontrolled, discrete systems, via Lyapunov's second method or Lyapunov's direct method. Our study included symbolic, bounded, statistical and hybrid model checking, through the open-source tools NuSMV, UCLID, S-TaLiRo and SpaceEx, respectively. Our experiments and results provide an insight on the strengths and limitations of these model checking approaches for the verification of control requirements for discrete systems at Simulink level. We found that statistical model checking with S-TaLiRo is the most suitable option to complement our previous work on automatic theorem proving.Comment: Submitted for review to European Control Conference 201