Stress Testing of Design Assumptions in Cyper-Physical Systems: A Control Theory-Based Approach

Cyber-Physical Systems (CPS) are most of the time safety-critical and expected to perform in uncertain environments. Therefore the identification of scenarios that prevent a CPS from performing according to its requirements is of fundamental importance. However, the multidisciplinary nature of CPS can make it difficult to identify such scenarios. In this article, we investigate the testing of CPS developed using control theory. In such systems, the software is developed collaboratively by control engineers and software engineers. When testing, it is important to account for this multidisciplinary development context. In particular, control engineers make design assumptions when contributing to system development in order to leverage control-theory and obtain guarantees on the CPS behaviour. However, such assumptions are not always satisfied in the implemented system and their falsification can lead to the loss of the control-theoretical guarantees. We define the problem of generating and identifying test cases that falsify such design assumptions as the stress testing of control-based CPS. Among the types of assumptions listed in the article, we focus on the use of linearised models of the physics. To generate test cases that falsify such assumptions, we leverage control theory to develop a qualitative characterisation of the input space of the control layer in CPS. We then propose a novel test case parametrisation for control-based CPS and use it together with the proposed characterisation to develop a testing approach aiming at falsifying the targeted assumptions. We evaluate our testing approach on six case studies including drone position control and continuous current motor control. Our results show that the proposed testing approach is effective at falsifying the linearity design assumption and the stress test cases can be used to highlight the causes of assumption violations.