Data-driven methods for statistical verification of uncertain nonlinear systems

Abstract

Due to the increasing complexity of autonomous, adaptive, and nonlinear systems, engineers commonly rely upon statistical techniques to verify that the closed-loop system satisfies specified performance requirements at all possible operating conditions. However, these techniques require a large number of simulations or experiments to exhaustively search the set of possible parametric uncertainties for conditions that lead to failure. This work focuses on resource-constrained applications, such as preliminary control system design or experimental testing, which cannot rely upon exhaustive search to analyze the robustness of the closed-loop system to those requirements. This thesis develops novel statistical verification frameworks that combine data-driven statistical learning techniques and control system verification. First, two frameworks are introduced for verification of deterministic systems with binary and non-binary evaluations of each trajectory's robustness. These frameworks implement machine learning models to learn and predict the satisfaction of the requirements over the entire set of possible parameters from a small set of simulations or experiments. In order to maximize prediction accuracy, closed-loop verification techniques are developed to iteratively select parameter settings for subsequent tests according to their expected improvement of the predictions. Second, extensions of the deterministic verification frameworks redevelop these procedures for stochastic systems and these new stochastic frameworks achieve similar improvements. Lastly, the thesis details a method for transferring information between simulators or from simulators to experiments. Moreover, this method is introduced as part of a new failure-adverse closed-loop verification framework, which is shown to successfully minimize the number of failures during experimental verification without undue conservativeness. Ultimately, these data-driven verification frameworks provide principled approaches for efficient verification of nonlinear systems at all stages in the control system development cycle.