Underminer: A Framework for Automatically Identifying Nonconverging Behaviors in Black-Box System Models

Evaluation of industrial embedded control system designs is a time-consuming and imperfect process. While an ideal process would apply a formal verification technique such as model checking or theorem proving, these techniques do not scale to industrial design problems, and it is often difficult to use these techniques to verify performance aspects of control system designs, such as stability or convergence. For industrial designs, engineers rely on testing processes to identify critical or unexpected behaviors. We propose a novel framework called Underminer to improve the testing process; this is an automated technique to identify nonconverging behaviors in embedded control system designs. Underminer treats the system as a black box and lets the designer indicate the model parameters, inputs, and outputs that are of interest. It differentiates convergent from nonconvergent behaviors using Convergence Classifier Functions (CCFs).

The tool can be applied in the context of testing models created late in the controller development stage, where it assumes that the given model displays mostly convergent behavior and learns a CCF in an unsupervised fashion from such convergent model behaviors. This CCF is then used to guide a thorough exploration of the model with the help of optimization-guided techniques or adaptive sampling techniques, with the goal of identifying rare nonconvergent model behaviors. Underminer can also be used early in the development stage, where models may have some significant nonconvergent behaviors. Here, the framework permits designers to indicate their mental model for convergence by labeling behaviors as convergent/nonconvergent and then constructs a CCF using a supervised learning technique. In this use case, the goal is to use the CCF to test an improved design for the model. Underminer supports a number of convergence-like notions, such as those based on Lyapunov analysis and temporal logic, and also CCFs learned directly from labeled output behaviors using machine-learning techniques such as support vector machines and neural networks. We demonstrate the efficacy of Underminer by evaluating its performance on several academic as well as industrial examples.