A robust and adaptive MPC formulation for Gaussian process models

2025-07-02

AI Summary

This paper addresses uncertain nonlinear systems subject to bounded disturbances and unmodeled nonlinear dynamics, proposing a robust adaptive model predictive control (MPC) framework. Methodologically, it pioneers the integration of contraction metrics into robust prediction using Gaussian process (GP) models, coupled with online GP learning for real-time model adaptation; probabilistic contraction constraints are formulated to rigorously ensure recursive feasibility, state convergence, and high-probability constraint satisfaction. Key contributions are: (1) the first application of contraction metrics in GP-based MPC for robust prediction under uncertainty; and (2) a unified analytical framework jointly characterizing uncertainty propagation and contraction-based control synthesis. Experimental validation on a quadrotor platform severely affected by ground effect disturbances demonstrates significant improvements in trajectory tracking accuracy and robustness against disturbances.

Technology Category

• Intelligent Robots: State Estimation
• Machine Learning: Calibration & Uncertainty Quantification
• Multiagent Systems: Multiagent Systems under Uncertainty

Application Category

• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

In this paper, we present a robust and adaptive model predictive control (MPC) framework for uncertain nonlinear systems affected by bounded disturbances and unmodeled nonlinearities. We use Gaussian Processes (GPs) to learn the uncertain dynamics based on noisy measurements, including those collected during system operation. As a key contribution, we derive robust predictions for GP models using contraction metrics, which are incorporated in the MPC formulation. The proposed design guarantees recursive feasibility, robust constraint satisfaction and convergence to a reference state, with high probability. We provide a numerical example of a planar quadrotor subject to difficult-to-model ground effects, which highlights significant improvements achieved through the proposed robust prediction method and through online learning.

Problem

• Robust adaptive MPC for uncertain nonlinear systems
• Gaussian Processes learn dynamics from noisy data
• Ensures feasibility, constraint satisfaction, and convergence

Innovation

• Robust adaptive MPC for Gaussian process models
• Uses contraction metrics for robust GP predictions
• Ensures feasibility and constraint satisfaction online