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.
In testing, inputs are applied to a system to stimulate actions and reactions, and outputs are observed to determine if the requirements are satisfied. The selection of inputs (test cases) needs to thoroughly explore the system's state space, whilst targeting its interesting regions (i.e., covering'' the system). Simulink is an ideal tool for testing models of control systems in simulation. Test generation systematically samples the state space of variables and parameters, e.g., through automated search @cite_11 .
@cite_11
2036657965
Search-based test-data generation has proved successful for code-level testing but almost no search-based work has been carried out at higher levels of abstraction. In this paper the application of such approaches at the higher levels of abstraction offered by MATLAB Simulink models is investigated and a wide-ranging framework for test-data generation and management is presented. Model-level analogues of code-level structural coverage criteria are presented and search-based approaches to achieving them are described. The paper also describes the first search-based approach to the generation of mutant-killing test data, addressing a fundamental limitation of mutation testing. Some problems remain whatever the level of abstraction considered. In particular, complexity introduced by the presence of persistent state when generating test sequences is as much a challenge at the Simulink model level as it has been found to be at the code level. The framework addresses this problem. Finally, a flexible approach to test sub-set extraction is presented, allowing testing resources to be deployed effectively and efficiently.