Scalable Optimization and Control (SOC) Lab

Research overview

Our research lies at the interface of optimization, control, and learning. We develop mathematical foundations and scalable algorithms for decision-making in dynamical systems, with applications to autonomous vehicles and traffic systems. Our current research is organized around five closely connected themes:

• Policy optimization and hidden convexity: We study the geometry of nonconvex policy optimization in optimal and robust control, with an emphasis on global optimality, strong duality, gradient dominance, and extended convex lifting.

• Nonsmooth optimization and proximal methods: We develop first-order, proximal, and bundle methods for weakly convex and nonsmooth problems, including policy optimization with stability and convergence guarantees.

• Scalable semidefinite and polynomial optimization: We exploit sparsity, low-rank structure, matrix decomposition, and regularity properties to design efficient algorithms for semidefinite, conic, and sum-of-squares optimization.

• Data-driven control and Koopman methods: We develop data-enabled predictive control and Koopman-based methods with formal guarantees on representation, stability, robustness, and online performance.

• Connected and autonomous vehicles: We use mixed traffic as an application testbed for scalable, data-driven, decentralized, and robust control.

Selected slides for these themes are available on the presentations page.

1. Policy optimization and hidden convexity

Many classical optimal and robust control problems are nonconvex in the policy space, yet their landscapes often possess strong global structure. We use convex reformulations and extended convex lifting to explain global optimality, strong duality, and gradient dominance in benchmark control problems.

Selected publications:

1. Yuto Watanabe, Yang Zheng. Gradient Dominance in the Linear Quadratic Regulator: A Unified Analysis for Continuous-Time and Discrete-Time Systems. Preprint, 2026.

2. Yuto Watanabe, Yang Zheng. Revisiting Strong Duality, Hidden Convexity, and Gradient Dominance in the Linear Quadratic Regulator. SIAM Journal on Control and Optimization, accepted, 2026.

3. Yang Zheng, Chih-Fan Pai, Yujie Tang. Benign Nonconvex Landscapes in Optimal and Robust Control, Part II: Extended Convex Lifting. IEEE Transactions on Automatic Control, accepted, 2026.

4. Yang Zheng, Chih-Fan Pai, Yujie Tang. Benign Nonconvex Landscapes in Optimal and Robust Control, Part I: Global Optimality. IEEE Transactions on Automatic Control, accepted, 2026.

2. Nonsmooth optimization and proximal methods

Weak convexity provides a useful bridge between nonsmooth nonconvex problems and tractable local models. We study subgradient, bundle, proximal point, and augmented Lagrangian methods, with an emphasis on explicit convergence rates and applications to control.

Selected publications:

1. Feng-Yi Liao, Yang Zheng. Revisiting Proximal Bundle Methods: Improved Rates under Hölder Smoothness. Preprint, 2026.

2. Yuto Watanabe, Feng-Yi Liao, Yang Zheng. Weak Convexity and Proximal Bundle Methods for Nonsmooth Policy Optimization in Robust Control. Preprint, 2026.

3. Feng-Yi Liao, Yang Zheng. A Proximal Descent Method for Minimizing Weakly Convex Optimization. Preprint, 2025.

4. Feng-Yi Liao, Lijun Ding, Yang Zheng. Error Bounds, PL Condition, and Quadratic Growth for Weakly Convex Functions, and Linear Convergences of Proximal Point Methods. Journal of Global Optimization, accepted, 2025.

3. Scalable semidefinite and polynomial optimization

Semidefinite and sum-of-squares optimization are powerful tools in control, machine learning, and operations research, but standard algorithms can be expensive at scale. We exploit chordal sparsity, low-rank solutions, cone approximations, and error-bound properties to build more scalable algorithms.

Selected publications:

1. Feng-Yi Liao, Lijun Ding, Yang Zheng. An Overview and Comparison of Spectral Bundle Methods for Primal and Dual Semidefinite Programs. Computational Optimization and Applications, accepted, 2025.

2. Feng-Yi Liao, Lijun Ding, Yang Zheng. Inexact Augmented Lagrangian Methods for Conic Programs: Quadratic Growth and Linear Convergence. Advances in Neural Information Processing Systems (NeurIPS), 2024.

3. Yang Zheng, Giovanni Fantuzzi. Sum-of-squares Chordal Decomposition for Polynomial Matrix Inequalities. Mathematical Programming, 197:71-108, 2023.

4. Yang Zheng, Aivar Sootla, Antonis Papachristodoulou. Block Factor-width-two Matrices and Their Applications to Semidefinite and Sum-of-squares Optimization. IEEE Transactions on Automatic Control, 68(2):943-958, 2023.

4. Data-driven control and Koopman methods

We study when data can provide useful representations of unknown dynamical systems and how those representations support reliable control. Current directions include data-enabled predictive control, Koopman linear embeddings, and stability guarantees for nonlinear systems.

Selected publications (newest first):

1. Xu Shang, Masih Haseli, Jorge Cortés, Yang Zheng. On the Existence of Koopman Linear Embeddings for Controlled Nonlinear Systems. Preprint, 2026.

2. Xu Shang, Jorge Cortés, Yang Zheng. On the Exponential Stability of Koopman Model Predictive Control. Learning for Dynamics and Control (L4DC), 2026.

3. Xu Shang, Yang Zheng. Regularization in Data-driven Predictive Control: A Convex Relaxation Perspective. Automatica, accepted, 2026.

5. Connected and autonomous vehicles in mixed traffic

Mixed traffic systems combine connected and autonomous vehicles with human-driven vehicles. We develop predictive and decentralized controllers that use a small number of autonomous vehicles to dissipate traffic waves, improve safety and efficiency, and remain robust to uncertain human-driving behavior.

Selected publications:

1. Xu Shang, Jiawei Wang, Yang Zheng. Decentralized Robust Data-driven Predictive Control for Smoothing Mixed Traffic Flow. IEEE Transactions on Intelligent Transportation Systems, accepted, 2024.

2. Jiawei Wang, Yang Zheng, Jianghong Dong, Chaoyi Chen, Mengchi Cai, Keqiang Li, Qing Xu. Implementation and Experimental Validation of Data-Driven Predictive Control for Dissipating Stop-and-Go Waves in Mixed Traffic. IEEE Internet of Things Journal, 2023.

3. Jiawei Wang, Yang Zheng, Keqiang Li, Qing Xu. DeeP-LCC: Data-EnablEd Predictive Leading Cruise Control in Mixed Traffic Flow. IEEE Transactions on Control Systems Technology, 2023.