Scalable Optimization and Control (SOC) Lab

Research overview

Our research lies in the interface of learning, optimization, and control of network systems, and their applications to cyber-physical systems, especially autonomous vehicles, and traffic systems. The goal is to develop computationally efficient and distributed solutions for large-scale network systems by exploring and exploiting real-world system structures. Our work has been integrating various mathematical, computational, and engineering tools to develop novel methods and frameworks for control and optimization. Most of our research is in one of the following directions:

• Data-driven and learning-based control: We consider both model-based and model-free control methods, and aim to establish formal guarantees on their sample efficiency, stability, and robustness.

• Scalable conic optimization: We try to exploit structures and sparsity of the problems and design more efficient algorithms for conic optimization, especially semidefinite programs (SDPs) and sum-of-squares (SOS) optimization.

• Scalable distributed control: We try to design approximation strategies (e.g., sparsity invariance) and take advantage of network structures (e.g., chordal decomposition) that make the design of distributed control scalable to large-scale instances.

• Connected and autonomous vehicles (CAVs): We try to 1) identify fundamental performance limits of linear control strategies for platooning of CAVs; 2) to reveal the fundamental ability of CAVs in shaping traffic flow and design traffic-oriented strategies for CAVs in mixed traffic systems.

1. Data-driven and learning-based control

In many practical applications, accurate system models are not known a priori. We aim to develop data-driven and learning-based control methods with formal performance guarantees. We use history and real-time data to update the system model with non-asymptotic finite-data guarantees (e.g., from contemporary high-dimensional statistics) and then explicitly consider model uncertainty estimates based on robust control. We also consider model-free methods to directly design control policies, where landscape properties of optimization problems are investigated. For both model-based and model-free methods, it is critical to establish formal guarantees on their sample efficiency, stability, and robustness.

Selected publications:

1. Yujie Tang*, Yang Zheng*, Na Li. Analysis of the Optimization Landscape of Linear Quadratic Gaussian (LQG) Control, Mathematical Programming, Series A (under review). A short version was accepted at L4DC, 2021 (* Equal contribution)

2. Yang Zheng*, Luca Furieri*, Maryam Kamgarpour, Na Li. Sample Complexity of Linear Quadratic Gaussian (LQG) Control for Output Feedback Systems. A short version was accepted at L4DC, 2021 (* Equal contribution)

3. Yang Zheng, Na Li. Non-asymptotic identification of linear dynamical systems using multiple trajectories. IEEE Control Systems Letters 5.5 (2020): 1693-1698.

4. Furieri, Luca, Yang Zheng, and Maryam Kamgarpour. “Learning the globally optimal distributed LQ regulator.” Learning for Dynamics and Control. PMLR, 2020. [arXiv]

2. Scalable conic optimization

Conic optimization is a powerful computational tool that has many applications, e.g., control theory, machine learning, and operations research. Most conic optimization problems can be solved in polynomial time using standard interior-point algorithms. However, these algorithms are only practical for small- to medium-sized problem instances. We try to exploit structures and sparsity of the problems and design more efficient algorithms for conic optimization, especially semidefinite programs (SDPs) and sum-of-squares (SOS) optimization.

Selected publications:

1. Zheng, Y., Fantuzzi, G. Sum-of-squares Chordal Decomposition for Polynomial Matrix Inequalities, Mathematical Programming, Series A, under review, 2020.

2. Zheng, Y., Fantuzzi, G., Papachristodoulou, A., Goulart, P., & Wynn, A. (2019). Chordal decomposition in operator-splitting methods for sparse semidefinite programs. Mathematical Programming, 1-44. [arXiv | Official Version]

3. Zheng, Y., Fantuzzi, G., & Papachristodoulou, A. (2018). Fast ADMM for sum-of-squares programs using partial orthogonality. IEEE Transactions on Automatic Control, 1-8. [arXiv | Official Version]

4. Zheng, Y., Fantuzzi, G., & Papachristodoulou, A. (2018). Sparse sum-of-squares (SOS) optimization: A bridge between DSOS/SDSOS and SOS optimization for sparse polynomials. arXiv preprint arXiv:1807.05463. [arXiv]

5. Zheng, Y., Fantuzzi, G., & Papachristodoulou, A. (2018). Decomposition methods for large-scale semidefinite programs with chordal aggregate sparsity and partial orthogonality. In Large-Scale and Distributed Optimization (pp. 33-55). Springer, Cham. [Official Version]

6. Ahmadi, A. A., Hall, G., Papachristodoulou, A., Saunderson, J., & Zheng, Y. (2017, December). Improving efficiency and scalability of sum of squares optimization: Recent advances and limitations. In 2017 IEEE 56th Annual Conference on Decision and Control (CDC) (pp. 453-462). IEEE. [Official Version]

3. Scalable distributed control

In network systems, a distributed control strategy is decided locally to govern global dynamics. This can be formulated as an optimization problem that minimizes a norm of the closed-loop system subject to a sparsity constraint on controller structure, which is NP-hard in general. We try to design approximation strategies (e.g., sparsity invariance) and take advantage of network structures (e.g., chordal decomposition) that make the design of distributed control scalable to large-scale instances.

Selected publications:

1. Zheng, Y., Kamgarpour, M., Sootla, A., & Papachristodoulou, A. (2019). Distributed Design for Decentralized Control using Chordal Decomposition and ADMM, IEEE Transactions on Control of Network Systems, to appear. [arXiv]

2. Zheng, Y., Mason, R. P., & Papachristodoulou, A. (2017). Scalable design of structured controllers using chordal decomposition. IEEE Transactions on Automatic Control, 63(3), 752-767. [arXiv | Official Version]

3. Zheng, Y., Furieri, L., Papachristodoulou, A., Li, N., & Kamgarpour, M. (2019). On the Equivalence of Youla, System-level and Input-output Parameterizations. arXiv preprint arXiv:1907.06256. [arXiv]

4. Furieri, L., Zheng, Y., Papachristodoulou, A., & Kamgarpour, M. (2019). Sparsity Invariance for Convex Design of Distributed Controllers. arXiv preprint arXiv:1906.06777. [arXiv]

5. Furieri, L., Zheng, Y., Papachristodoulou, A., & Kamgarpour, M. (2019). An Input-Output Parametrization of Stabilizing Controllers: amidst Youla and System Level Synthesis. IEEE Control Systems Letters. [arXiv | Official Version]

4. Connected and autonomous vehicles (CAVs)

The emergence of connected and autonomous vehicles (CAVs) promises to revolutionize the road transportation systems. We focus on two particular applications: 1) platooning of multiple CAVs, and 2) mixed traffic systems consisting of both CAVs and human-driven vehicles. In platooning of CAVs, we try to identify fundamental performance limits of linear control strategies and design advanced control strategies (e.g, model predictive control and robust control) with safety and robustness guarantees. In mixed traffic systems, we try to reveal the fundamental ability of CAVs in shaping traffic flow and design traffic-oriented strategies for CAVs.

Selected publications:

1. Wang, J., Zheng, Y., Chen, C., Xu, Q., & Li, K. (2021). Leading cruise control in mixed traffic flow: System modeling, controllability, and string stability. IEEE Transactions on Intelligent Transportation Systems. [arXiv]

2. Zheng, Y., Wang, J., & Li, K. (2018). Smoothing traffic flow via control of autonomous vehicles. arXiv preprint arXiv:1812.09544. [arXiv]

3. Zheng, Y., Li, S. E., Li, K., & Ren, W. (2017). Platooning of connected vehicles with undirected topologies: Robustness analysis and distributed H-infinity controller synthesis. IEEE Transactions on Intelligent Transportation Systems, 19(5), 1353-1364. [arXiv |Official version]

4. Zheng, Y., Li, S. E., Li, K., Borrelli, F., & Hedrick, J. K. (2016). Distributed model predictive control for heterogeneous vehicle platoons under unidirectional topologies. IEEE Transactions on Control Systems Technology, 25(3), 899-910. [Official version]

5. Zheng, Y., Li, S. E., Wang, J., Cao, D., & Li, K. (2016). Stability and scalability of homogeneous vehicular platoon: Study on the influence of information flow topologies. IEEE Transactions on Intelligent Transportation Systems, 17(1), 14-26. [Official version]

6. Zheng, Y., Li, S. E., Li, K., & Wang, L. Y. (2016). Stability margin improvement of vehicular platoon considering undirected topology and asymmetric control. IEEE Transactions on Control Systems Technology, 24(4), 1253-1265. [Official version]