Control Of Uncertain Nonlinear Systems Using Non-parametric Machine Learning

Abstract

Accurately modeling nonlinear dynamical systems is challenging due to model inaccuracies and uncertainties, which can significantly degrade controller performance. Designing stabilizing controllers for nonlinear systems under such uncertainties remains a challenging problem. A wide range of stabilizing control algorithms have been proposed in the existing literature; however, their effectiveness relies on the accuracy of system dynamics. This manuscript addresses the issue of stabilizing controller design for nonlinear systems, particularly when the drift vector field is uncertain, by integrating non-parametric machine learning techniques to estimate the unknown component. In this work, a framework is proposed in which Gaussian process regression (GPR) is employed to estimate the unknown drift vector field and integrate it into the control synthesis. Moreover, an event-triggered condition is employed to collect data online as needed. The proposed approach enables the construction of control laws that practically stabilize the system, despite incomplete system knowledge. Rigorous theoretical guarantees for the proposed method are provided, and the effectiveness of the framework is demonstrated through numerical simulation studies.