Testing Autonomous Cyber-Physical Systems with Koopman Surrogate Model Predictive Control

Cyber-physical systems (CPSs) are on the rise for safety-critical applications. While formal verification approaches may work on simple systems, these approaches need more scalability. When systems are sufficiently complex, testing is often the only practical way to gain confidence the system works as expected. How can we generate high-quality tests for CPS? This work proposes an approach to improve test case generation for CPSs. We achieve this by proposing a new model-based seed generation algorithm in the fuzz testing pipeline. We first use the Koopman operator technique to construct a predictor model to capture the effect of time-varying inputs on the CPS behavior. Then, we use the model in a Model Predictive Control (MPC) optimization loop, generating control inputs that drive the system through state space. We evaluate the strategy's effectiveness through extensive experiments on the well-known neural network air-To-Air collision avoidance benchmark, ACAS Xu. Evaluation results prove that the proposed Koopman MPC approach achieves better test coverage than other fuzz testing and falsification tools.