Towards safe and tractable Gaussian process-based MPC: Efficient sampling within a sequential quadratic programming framework
This work addresses safety and efficiency issues in control systems for real-world applications, representing an incremental improvement over existing GP-MPC methods.
The paper tackles the challenge of balancing computational tractability and safety guarantees in Gaussian process-based model predictive control (GP-MPC) by proposing a robust formulation that ensures constraint satisfaction with high probability. It introduces a sampling-based approach within a sequential quadratic programming framework, demonstrating improved reachable set approximations and real-time feasibility in numerical examples.
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.