Testing Cyber-Physical Systems through Bayesian Optimization

Jyotirmoy V. Deshmukh, Marko Horvat, Xiaoqing Jin, Rupak Majumdar, Vinayak S. Prabhu

Abstract: Many problems in the design and analysis of cyber-physical systems (CPS) reduce to the following optimization problem: given a CPS which transforms continuous-time input traces in Rm to continuous-time output traces in Rn and a cost function over output traces, find an input trace which minimizes the cost. Cyber-physical systems are typically so complex that solving the optimization problem analytically by examining the system dynamics is not feasible. We consider a black-box approach, where the optimization is performed by testing the input-output behaviour of the CPS. We provide a unified, tool-supported methodology for CPS testing and optimization. Our tool is the first CPS testing tool that supports Bayesian optimization. It is also the first to employ fully automated dimensionality reduction techniques. We demonstrate the potential of our tool by running experiments on multiple industrial case studies. We compare the effectiveness of Bayesian optimization to state-of-the-art testing techniques based on CMA-ES and Simulated Annealing.