Testing CPS with Design Assumptions-Based Metamorphic Relations and Genetic Programming

Cyber-Physical Systems (CPSs) software is used to enforce desired behaviours on physical systems. To test the interaction between the CPS software and the system's physics, engineers provide traces of desired physical states and observe traces of the actual physical states. CPS requirements describe how closely the actual physical traces should track the desired traces. These requirements are typically defined for specific, simple input traces such as step or ramp sequences, and thus are not applicable to arbitrary inputs. This limits the availability of oracles for CPSs. Our recent work proposes an approach to testing CPS using control-theoretical design assumptions instead of requirements. This approach circumvents the oracle problem by leveraging the control-theoretical guarantees that are provided when the design assumptions are satisfied. To address the test case generation and oracle problems, researchers have proposed metamorphic testing, which is based on the study of relations across tests, i.e., metamorphic relations (MRs). In this work, we define MRs based on the design assumptions and explore combinations of these MRs using genetic programming to generate CPS test cases. This enables the generation of CPS input traces with potentially arbitrary shapes, together with associated expected output traces. We use the deviation from the expected output traces to guide the generation of input traces that falsify the MRs. Our experiment results show that the MR-falsification provides engineers with new information, helping them identify passed and failed test cases. Furthermore, we show that the generation of traces that falsify the MRs is a non-trivial problem, which is successfully addressed by our genetic search.