Contextual Control: Integrating Learning, Optimization, and Physical Structures in Control Systems

Reliable data-driven control must provide closed-loop guarantees—on stability, performance, safety—by generalizing across an entire domain from finite samples of the dynamics. In learning theory, this is usually achieved via the introduction of an inductive bias, that is, a set of structural assumptions placed on the problem to connect sampled and unsampled data. While inductive biases for classification and regression problems have been widely studied and their performance is well understood, much less is known for control tasks. This raises a central question: which inductive bias enables efficient nonlinear control with rigorous guarantees on stability, safety, and optimality?

For Lipschitz continuous vector fields, a common assumption (or inductive bias) in control, we construct behavioral guarantees by combining local improvement conditions—integral Lyapunov-like conditions or Bellman inequalities—with coverage arguments over the state space that render such behavior recurrent. This viewpoint enables data-driven verification, but also inspires a novel class of nonparametric controllers, called here chain policies, which are akin to action chunking but with variable duration, and compose a sequence of locally verified controls (a chain) into globally valid certifiable policies. We apply these ideas to data-driven stabilization and to the acceleration of model predictive control, where performance can be systematically traded for reduced data requirements.

Notably, this Lipschitz viewpoint, while flexible, is very conservative: its worst-case bounds still require dense coverage of the state space, a demand that scales poorly with state dimension. To overcome this limitation, we turn to Hamiltonian dynamics, which offer a structurally different inductive bias based on energy and volume conservation. These conservation laws imply, via the Poincaré recurrence theorem, that every region visited by a trajectory is revisited infinitely often, providing vast opportunities for generalization. This allows us to construct chain policies for target reachability from remarkably small datasets.

Enrique Mallada is an Associate Professor of Electrical and Computer Engineering at Johns Hopkins University, where he has been a faculty member since 2016. He received his Ph.D. in Electrical and Computer Engineering with a minor in Applied Mathematics from Cornell University and a Telecommunications Engineering degree from ORT University, Uruguay. Before joining Hopkins, he was a Postdoctoral Fellow at Caltech’s Center for the Mathematics of Information. His honors include the Johns Hopkins Alumni Association Teaching Award (2021), NSF CAREER Award (2018), Caltech’s CMI Fellowship (2014), and Cornell ECE Director’s Thesis Award (2014). His research spans control, dynamical systems, and optimization, with applications to safety-critical systems, networks, and power grids.

Learning dynamical models from high-dimensional observations (e.g., images) is central to deploying model predictive control (MPC) when the system state is not directly observed. Recent latent predictive approaches, including joint-embedding predictive architectures (JEPAs), learn compact state representations for prediction and planning without reconstruction. However, these representations are often sensitive to nuisance variations—such as background changes or visual distractors—leading to degraded closed-loop performance under distribution shift. We address this by augmenting the predictive objective with a bisimulation-based constraint that enforces control-relevant state abstraction: observations with similar transition dynamics and outcomes are mapped to nearby latent states. This yields representations better aligned with MPC, filtering out control-irrelevant variability while preserving predictive structure. Across all benchmarks, our model consistently improves robustness to slow features while operating in a reduced latent space, up to 10× smaller than that of DINO-WM.

James Anderson is an Associate Professor of Electrical Engineering at Columbia University and is also a member of the Data Science Institute. From 2016 to 2019, he was a senior postdoctoral scholar in the Department of Computing + Mathematical Sciences at the California Institute of Technology. Prior to Caltech, he held a Junior Research Fellowship at St John’s College, University of Oxford, and was affiliated with the Department of Engineering Science. He received his DPhil (PhD) from Oxford in 2012 and his BSc and MSc degrees from the University of Reading in 2005 and 2006, respectively. His research spans control, learning theory, and optimization, with applications in smart grids and energy markets. Together with his students and collaborators, he has received several best paper awards in venues such as the IEEE Transactions on Control of Network Systems, the IEEE Conference on Decision and Control, and the Learning for Dynamics and Control Conference.

Modern networked control systems increasingly act on short-horizon disturbance forecasts produced by learned models. Three difficulties arise together: the nodal disturbance is a superposition of heterogeneous contextual sources with distinct spatial-temporal dynamics, coordination across nodes is restricted by limited communication, and the forecasts themselves degrade unpredictably. This talk develops a unified framework where a convex reparameterization of predictive controllers makes explicit the effects of communication structure and reliance on predictions on the closed-loop system.

First, we will describe the offline synthesis of localized predictive controllers that admits a novel regret bound exposing a non-monotonic trade-off between communication range and prediction error. Then we develop an online projected gradient-based controller that converges to the hindsight optimum policy and adapts agent-wise trust at the resolution of individual coordinates under heterogeneous prediction quality. Finally, we demonstrate a voltage control application where disentangling the forecasted contextual sources of each nodal disturbance, combined with online confidence learning, yields input-to-state stability on a real microgrid.

Jing Yu is an Assistant Professor in the Department of Electrical and Computer Engineering at the University of Washington, where she is also an affiliate faculty member with the Clean Energy Institute. Before joining UW, she was a postdoctoral researcher at the University of Illinois Urbana-Champaign and the University of Michigan. She received her Ph.D. in Control and Dynamical Systems from Caltech. Her work has been recognized by awards including the Caltech CMS Amori Doctoral Prize and the ACM SIGEnergy Doctoral Dissertation Award Honorable Mention.

In this talk, we present a set of tools and methodologies on physics-informed Neural Operator Control (NOC) for nonlinear systems. Specifically, we will present NOC for predictor feedback in nonlinear delay systems and NOC for optimal motion planning.

The first part of the talk is about NOC for predictor feedback in nonlinear delay systems. Predictor feedback is effective for delay compensation, yet a critical challenge lies on efficient computation of the predictor operator. We introduce NOC for approximating the nonlinear predictor mapping and prove semiglobal practical stability (dependent on the learning error) of the proposed NOC predictor feedback via back-stepping transformation.

The second part of the talk is about NOC for motion planning. We design physics-informed NOC for optimal motion planning and control in highly dynamic environments. We propose to encode the obstacle geometries as cost functions and produce fast value function approximations for motion planning, which is defined by the Eikonal partial differential equation (PDE).

Yuanyuan Shi is an Assistant Professor of Electrical and Computer Engineering at the University of California San Diego. She received her Ph.D. in Electrical and Computer Engineering from the University of Washington, Seattle, in 2020. From 2020 to 2021, she was a Postdoctoral Scholar at Caltech. Her research focuses on machine learning, dynamical systems and control, with applications to sustainable power and energy systems. She received the inaugural Anastasio Early Career Faculty Scholar from Los Alamos National Lab, an NSF CAREER Award, a Schmidt Sciences AI2050 Early Career Fellowship, and best paper finalists in L4DC 2025 and ACM e-Energy 2022.

The topology and physics of a networked system are a powerful inductive bias for control design. This talk argues that exploiting them, rather than designing around them, allows simple physical models to be translated directly into simple, scalable, and often globally optimal control laws. I will draw examples from our recent work on passive and reciprocal networks, on sparsity-preserving optimal control, and on the interface with data-driven methods, with an emphasis on what the workshop's themes of context and adaptation add to the picture.

Richard Pates received the M.Eng degree in 2009, and the Ph.D. degree in 2014, both from the University of Cambridge. He is currently a Senior Lecturer at Lund University. His research interests include modular methods for control system design, stability and control of electrical power systems, and fundamental performance limitations in large-scale systems.

Traffic flow systems exhibit complex spatiotemporal dynamics driven by nonlinear vehicle interactions, heterogeneous driving behaviors, and uncertain demand patterns. Partial differential equation models are employed as macroscopic framework for describing these dynamics and for designing traffic estimation and control strategies. This talk will discuss learning-enabled PDE modeling and control methods for traffic flow systems, with an emphasis on integrating physical traffic flow models, control theory, and machine learning. The talk will begin with PDE backstepping control for stop-and-go congestion mitigation. It will then discuss how physics-informed neural networks can be used for traffic flow modeling and state estimation, particularly when sensing data are sparse, noisy, and partially observed. Finally, the talk will present neural operator approaches for accelerating PDE control design, enabling fast approximation of control kernels and feedback laws. Through these topics, the talk aims to highlight how learning methods can enhance PDE-based traffic modeling, estimation, and control, and how the integration of machine learning with rigorous control-theoretic tools can support reliable and scalable traffic management for future intelligent transportation systems.

Dr. Huan Yu is an Assistant Professor at the Hong Kong University of Science and Technology (Guangzhou), jointly appointed with the Intelligent Transportation and Robotics & Autonomous Systems Thrusts. She received the B.Sc. degree from Northwestern Polytechnical University, and the M.Sc. and Ph.D. degrees in Aerospace Engineering from the Department of Mechanical and Aerospace Engineering, University of California, San Diego. She was a visiting scholar at University of California, Berkeley and Massachusetts Institute of Technology. Her research integrates control theory, transportation science, and machine learning, with applications for urban mobility systems.

Many optimal and robust control problems are nonconvex and potentially nonsmooth in their policy optimization forms. In this talk, we present the Extended Convex Lifting (ECL) framework, which reveals hidden convexity in classical optimal and robust control problems from a modern optimization perspective. The proposed ECL framework offers a bridge between nonconvex policy optimization and convex reformulations. Despite non-convexity and non-smoothness, the existence of an ECL not only guarantees convex reformulation of the policy optimization problem, but also certifies a class of first-order non-degenerate stationary points to be globally optimal. We further give some examples of benchmark control problems that can be encompassed and analyzed by this ECL framework. We also expect that ECL will be of independent interest for analyzing nonconvex problems beyond control.

Yujie Tang received the bachelor’s degree in electronic engineering from Tsinghua University, Beijing, China, in 2013, and the Ph.D. degree in electrical engineering from the California Institute of Technology, Pasadena, CA, USA, in 2019. He is currently an Assistant Professor with the School of Advanced Manufacturing and Robotics, Peking University, Beijing. Before joining Peking University, he was a Postdoctoral Fellow with the School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, USA. His research interests include distributed optimization, control and learning, and their applications in large-scale cyber-physical networks.

Constrained policy optimization is a central methodology in reinforcement learning for optimizing policies subject to explicit requirements. Its applications span a wide range of domains, from robot navigation to health care. However, Lagrangian-based policy gradient methods exhibit oscillatory training behavior due to the underlying minimax structure, posing a major challenge for stable policy learning. This talk discusses two approaches to mitigating such oscillations. First, I will introduce regularization into Lagrangian-based constrained minimax optimization and present a regularized policy-gradient primal-dual method with sublinear convergence guarantees for the policy iterates. Second, I will introduce optimism, a technique inspired by learning in games, to develop an optimistic gradient-based primal-dual method. This method achieves linear convergence of the policy iterates to an optimal policy, highlighting the effectiveness of optimism even in nonconvex minimax optimization settings. Together, these results clarify the roles of regularization and optimism in stabilizing constrained policy learning.

Dongsheng Ding is an Assistant Professor of Electrical Engineering and Computer Science at the University of Tennessee, Knoxville, and a member of AI Tennessee. From 2022 to 2025, he was a Postdoctoral Researcher in the Department of Electrical and Systems Engineering at the University of Pennsylvania. He received his Ph.D. in Electrical Engineering from the University of Southern California in 2022. His research applies principles and tools from optimization and control to the study of requirement-driven machine decision-making. His recent work develops methods that enable reinforcement learning and generative models to operate under explicit requirements, including safety and fairness. He is a recipient of the UTK GenAI Faculty Fellowship, the NeurIPS Scholar Award, and ICML Expert Reviewer recognition.

Graphical characterizations of uni-variable systems, such as Nyquist and Bode diagrams, are taught in almost all control curricula and widely used across engineering domains. These tools are intuitive and informative, enabling many closed-loop properties, including stability and robustness, to be inferred by inspection. However, for multivariable systems, the coupling of multi-dimensional information poses challenges as well as opens up many possibilities for extending such graphical tools. In this talk, we will examine several emerging tools developed in this direction, including the scaled relative graph and the Davis–Wielandt shell, along with their associated feedback stability certificates. In particular, we will highlight the connections among these tools and their relationship to quadratic separations. We will also outline the key ideas behind their visualization and the validation of their resulting robust stability conditions. Finally, we will present a case study on congestion control protocols and discuss how scalability could be incorporated into these tools for analyzing large-scale networked systems.

Ding Zhang is a Research Fellow at The Australian National University. He received the B.Eng. degree in Mechanical Engineering from Huazhong University of Science and Technology, Wuhan, China, and the Ph.D. degree in Electronic and Computer Engineering from The Hong Kong University of Science and Technology, Hong Kong SAR, where he also worked as a Postdoctoral Research Fellow. He was a visiting student with the EMAN Group at King Abdullah University of Science and Technology, Thuwal, Saudi Arabia, and with the Control Group at University of Cambridge, Cambridge, United Kingdom. His research focuses on graphical stability analysis of large-scale networked systems, with broader interests in matrix theory, spectral graph theory, and control theory.