7 papers
Regularization in Data-driven Predictive Control: A Convex Relaxation Perspective
Xu Shang, Yang Zheng
This paper explores the role of regularization in data-driven predictive control (DDPC) through the lens of convex relaxation. Using a bi-level optimization framework, we model sys…
Online Tracking with Predictions for Nonlinear Systems with Koopman Linear Embedding
Chih-Fan Pai, Xu Shang, Jiachen Qian +1
We study the problem of online tracking in unknown nonlinear dynamical systems, where only short-horizon predictions of future target states are available. This setting arises in p…
On the Existence of Koopman Linear Embeddings for Controlled Nonlinear Systems
Xu Shang, Masih Haseli, Jorge Cortés +1
Koopman linear representations have become a popular tool for control design of nonlinear systems, yet it remains unclear when such representations are exact. In this paper, we est…
On the Exponential Stability of Koopman Model Predictive Control
Xu Shang, Jorge Cortés, Yang Zheng
Koopman Model Predictive Control (MPC) uses a lifted linear predictor to efficiently handle constrained nonlinear systems. While constraint satisfaction and (practical) asymptotic…
Dictionary-free Koopman Predictive Control for Autonomous Vehicles in Mixed Traffic
Xu Shang, Zhaojian Li, Yang Zheng
Koopman Model Predictive Control (KMPC) and Data-EnablEd Predictive Control (DeePC) use linear models to approximate nonlinear systems and integrate them with predictive control. B…
Willems' Fundamental Lemma for Nonlinear Systems with Koopman Linear Embedding
Xu Shang, Jorge Cortés, Yang Zheng
Koopman operator theory and Willems' fundamental lemma both can provide (approximated) data-driven linear representation for nonlinear systems. However, choosing lifting functions…