Learning-Based Non-Linear Model Predictive Control with Gaussian Processes: A Computational Efficiency Analysis of open-source toolboxes

This work investigates the computational efficiency in Learning-Based Non-Linear Model Predictive Control (NMPC) with Gaussian Processes (GPs), focusing on the comparison of two open-source toolboxes: L4ACADOS and LbMATMPC. NMPC methods augmented with GPs enable accurate modeling of unknown dynamics enabling precise modeling of the real system dynamics but are computationally demanding, especially as the volume of training data increases. A key challenge is the growth in computational time associated with GP inference as the dataset size expands causing. This work evaluates how GPU acceleration and dimensionality reduction techniques can mitigate these limitations. The study compares different approaches employed by these two toolboxes. A shared toy problem serves as the benchmark, allowing consistent evaluation of computation times, particularly that of sequential quadratic programming iterations. Results highlight that GPU acceleration significantly reduces the computational overhead of GP computations, making real-time NMPC feasible for large datasets, once the dataset size reaches a threshold where the GPU's initial overhead is outweighed by its processing efficiency. Additionally, dimensionality reduction methods, including sparse GP approximations via Stochastic Variational Gaussian Processes, are tested to explore whether comparable performance can be achieved with fewer training points. These techniques may obviate the need for extensive datasets, further reducing the computational burden and questioning the necessity of GPU acceleration in certain cases. The findings provide insights into the trade-offs between GP model accuracy, computational efficiency, and hardware requirements in learning-based NMPC. By leveraging both GPU acceleration and advanced GP approximation techniques, this thesis aims to advance the practical deployment of efficient NMPC strategies in real-world applications.