Tube-Based Model Predictive Control with Random Fourier Features for Nonlinear Systems

TL;DR

This paper introduces a novel control approach combining Random Fourier Features with tube-based Model Predictive Control to efficiently handle nonlinear systems, reducing conservativeness and errors while ensuring robustness and real-time performance.

Contribution

It develops an RFF-based residual learning method integrated with tube MPC, providing a computationally efficient and robust control framework for nonlinear systems.

Findings

Reduces tube size by approximately 50% compared to linear baseline.

Achieves around 70% smaller errors in autonomous vehicle path-tracking.

Maintains real-time performance with provable robustness guarantees.

Abstract

This paper presents a computationally efficient approach for robust Model Predictive Control of nonlinear systems by combining Random Fourier Features with tube-based MPC. Tube-based Model Predictive Control provides robust constraint satisfaction under bounded model uncertainties arising from approximation errors and external disturbances. The Random Fourier Features method approximates nonlinear system dynamics by solving a numerically tractable least-squares problem, thereby reducing the approximation error. We develop the integration of RFF-based residual learning with tube MPC and demonstrate its application to an autonomous vehicle path-tracking problem using a nonlinear bicycle model. Compared to the linear baseline, the proposed method reduces the tube size by approximately 50%, leading to less conservative behavior and resulting in around 70% smaller errors in the test scenario. Furthermore, the proposed method achieves real-time performance while maintaining provable robustness guarantees.