# Linearized Gaussian Processes for Fast Data-driven Model Predictive Control

## TL;DR

This paper introduces a linearized Gaussian Process approach combined with Sequential Convex Programming to enhance the speed and scalability of Gaussian Process-based Model Predictive Control, making it more suitable for real-time applications.

## Contribution

The paper proposes a novel linearized Gaussian Process method with Sequential Convex Programming to significantly improve GP-based MPC's computational efficiency and scalability.

## Key findings

- The new method is faster than existing GP-MPC approaches.
- It scales better with larger models and maintains predictable performance.
- Demonstrated effectiveness in a numerical example.

## Abstract

Data-driven Model Predictive Control (MPC), where the system model is learned from data with machine learning, has recently gained increasing interests in the control community. Gaussian Processes (GP), as a type of statistical models, are particularly attractive due to their modeling flexibility and their ability to provide probabilistic estimates of prediction uncertainty. GP-based MPC has been developed and applied, however the optimization problem is typically non-convex and highly demanding, and scales poorly with model size. This causes unsatisfactory solving performance, even with state-of-the-art solvers, and makes the approach less suitable for real-time control. We develop a method based on a new concept, called linearized Gaussian Process, and Sequential Convex Programming, that can significantly improve the solving performance of GP-based MPC. Our method is not only faster but also much more scalable and predictable than other commonly used methods, as it is much less influenced by the model size. The efficiency and advantages of the algorithm are demonstrated clearly in a numerical example.