Verifying Spatiotemporal Systems via Robustness Bounds: An Application to Unmanned Underwater Vehicles

Abstract

The authors present an approach for verifying computer simulations for spatiotemporal systems. Specifically, the goal is to confirm that the computer simulation for a linear controller of an Unmanned Underwater Vehicle (UUV) correctly captures key elements of a conceptual model for the UUV controller. The key elements considered are stability and robustness of the UUV’s control system model. Here, stability refers to asymptotic stability of the model’s state variables, assuming bounded input parameters. Robustness refers to the model’s ability to handle uncertainty in these parameters. The verification is performed in two steps. First, for a fixed UUV controller, a maximum range of uncertain parameters is found and for that entire range confirmed that the computer simulation remains stable as required by the conceptual model. Next, a combination of control cost function and range of uncertain parameters is optimized while maintaining UUV stability, again, for the entire range of uncertainty and as required by the conceptual model. In both steps, independent Monte-Carlo simulations are performed to confirm the verification.