Evaluating MR-GPR and MR-NN: An Exploration of Data-driven Control Methods for Nonlinear Systems

This paper addresses the challenge of data-driven control of nonlinear systems, focusing on the limitations and capabilities of model reference Gaussian process regression (MR-GPR) and its evolved counterpart, model reference neural networks (MR-NN). MR-GPR, based on Gaussian processes renowned for their adaptability to diverse data structures, encounters scalability issues especially when handling large datasets. To address these limitations, this paper introduces MR-NN, an extension of MR-GPR, leveraging neural networks (NN) to manage large datasets and capture complex nonlinear dynamics effectively. We present a comprehensive evaluation of both methods through a classical control problem of the inverted pendulum, a system well-recognized for its nonlinear behavior. Numerical experiments are conducted to compare the methods in terms of control performance, computational efficiency, and reliability.