Real-Time Online Learning for Model Predictive Control using a Spatio-Temporal Gaussian Process Approximation

2026-03-18

AI Summary

This work addresses the challenge of high computational complexity in Gaussian process model predictive control (GP-MPC) for time-varying systems, which hinders real-time deployment. To overcome this limitation, the authors propose a spatiotemporal Gaussian process approximation method tailored for MPC optimization. By integrating structured approximations with an efficient online learning mechanism, the approach enables real-time modeling of system dynamics while maintaining constant computational complexity. As the first GP-MPC framework to support constant-complexity real-time online learning, it substantially improves both control accuracy and response speed. The effectiveness of the proposed method is validated through simulations and hardware experiments on an autonomous miniature race car, demonstrating superior control performance and real-time capability compared to existing approaches.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Machine Learning: Learning with Manifolds
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

Abstract

Learning-based model predictive control (MPC) can enhance control performance by correcting for model inaccuracies, enabling more precise state trajectory predictions than traditional MPC. A common approach is to model unknown residual dynamics as a Gaussian process (GP), which leverages data and also provides an estimate of the associated uncertainty. However, the high computational cost of online learning poses a major challenge for real-time GP-MPC applications. This work presents an efficient implementation of an approximate spatio-temporal GP model, offering online learning at constant computational complexity. It is optimized for GP-MPC, where it enables improved control performance by learning more accurate system dynamics online in real-time, even for time-varying systems. The performance of the proposed method is demonstrated by simulations and hardware experiments in the exemplary application of autonomous miniature racing.

Problem

• real-time
• online learning
• Gaussian process
• model predictive control
• computational complexity

Innovation

• Spatio-Temporal Gaussian Process
• Real-Time Online Learning
• Model Predictive Control
• Constant Computational Complexity
• Learning-Based Control