2 citations · 5 across the 10 of their papers we have counts for
10 papers
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…
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…
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…
Decentralized Robust Data-driven Predictive Control for Smoothing Mixed Traffic Flow
Xu Shang, Jiawei Wang, Yang Zheng
In a mixed traffic with connected automated vehicles (CAVs) and human-driven vehicles (HDVs) coexisting, data-driven predictive control of CAVs promises system-wide traffic perform…
Convex Approximations for a Bi-level Formulation of Data-Enabled Predictive Control
Xu Shang, Yang Zheng
The Willems' fundamental lemma, which characterizes linear time-invariant (LTI) systems using input and output trajectories, has found many successful applications. Combining this…
Smoothing Mixed Traffic with Robust Data-driven Predictive Control for Connected and Autonomous Vehicles
Xu Shang, Jiawei Wang, Yang Zheng
The recently developed DeeP-LCC (Data-EnablEd Predictive Leading Cruise Control) method has shown promising performance for data-driven predictive control of Connected and Autonomo…
Controlled scaling of Hilbert space frames for R^2
Peter Casazza, Shang Xu
A Hilbert space frame on is {\it scalable} if we can scale the vectors to make them a tight frame. There are known classifications of scalable frames. There are two basic que…