Stochastic Error Bounds in Nonlinear Model Predictive Control with Gaussian Processes via Parameter-Varying Embeddings

TL;DR

This paper develops stochastic error bounds for nonlinear systems controlled by LPV-MPC using Gaussian Processes, improving robustness and reducing conservatism compared to deterministic methods.

Contribution

It introduces a stochastic error bounding method for LPV-MPC with GPs, enhancing uncertainty quantification and robustness in nonlinear control.

Findings

Improved robustness over deterministic approaches

Reduced conservatism in error bounds

Validated on unbalanced disk regulator problem

Abstract

This study utilized the Gaussian Processes (GPs) regression framework to establish stochastic error bounds between the actual and predicted state evolution of nonlinear systems. These systems are embedded in the linear parameter-varying (LPV) formulation and controlled using model predictive control (MPC). Our main focus is quantifying the uncertainty of the LPVMPC framework's forward error resulting from scheduling signal estimation mismatch. We compared our stochastic approach with a recent deterministic approach and observed improvements in conservatism and robustness. To validate our analysis and method, we solved the regulator problem of an unbalanced disk.