Towards safe and tractable Gaussian process-based MPC: Efficient sampling within a sequential quadratic programming framework

TL;DR

This paper introduces a robust Gaussian process-based model predictive control method that ensures safety constraints with high probability, using an efficient sampling approach within a sequential quadratic programming framework for real-time applications.

Contribution

It proposes a novel sampling-based GP-MPC formulation that guarantees safety and improves reachable set approximation while maintaining computational efficiency.

Findings

Enhanced reachable set approximation over existing methods

Real-time feasible computation times demonstrated

High probability safety guarantees achieved

Abstract

Learning uncertain dynamics models using Gaussian process~(GP) regression has been demonstrated to enable high-performance and safety-aware control strategies for challenging real-world applications. Yet, for computational tractability, most approaches for Gaussian process-based model predictive control (GP-MPC) are based on approximations of the reachable set that are either overly conservative or impede the controller's safety guarantees. To address these challenges, we propose a robust GP-MPC formulation that guarantees constraint satisfaction with high probability. For its tractable implementation, we propose a sampling-based GP-MPC approach that iteratively generates consistent dynamics samples from the GP within a sequential quadratic programming framework. We highlight the improved reachable set approximation compared to existing methods, as well as real-time feasible computation times, using two numerical examples.