Towards nonlinear model predictive control of flexible structures using Gaussian Processes

In recent years, there is a growing interest of using and implementing data driven control in structural dynamics. This study considers applying Nonlinear Model Predictive Control (NMPC) to flexible structures by utilising recent developments in models which have been learnt from example data, i.e. machine learning approaches. The Gaussian process (GP) is a Bayesian machine learning algorithm identified for use as a black-box model in NMPC; it provides both the prediction of the system output and the associated confidence. In a control context, a GP can be utilised as a discrepancy model for linear or nonlinear flexible dynamic structures within MPC or even as the nonlinear model of the system itself. The Nonlinear Output Error model (GP-NOE) is a popular GP structure for dynamic systems that is utilised in predictive control strategies and requires predictions to be propagated to the control horizon. This novel framework is evaluated on a cantilever beam with light damping, and the results demonstrate robust control performance in both tracking and regulator tasks. The positive results inspire additional investigation into the proposed technique, particularly in the setting of a fully nonlinear system with unknown dynamics, such as an actuator within the flexible structure.