IEEE Conference on Decision and Control · CDC 2026 · Tutorial Session
Learning and Control Beyond Linearity
Towards a Non-asymptotic Theory for Bilinear Systems
About the tutorial
Overview
This tutorial provides a unified view of the emerging area of bilinear learning and control. Using linear systems as a benchmark, it explains what fundamentally changes in the bilinear settings, how recent theory addresses finite-sample learning and control, and how these ideas connect to broader themes in nonlinear control, representation learning, and data-driven decision making. For learning, we emphasize tools that are particularly useful in the bilinear settings, such as one-sided Bernstein's inequality for dependent and heavy-tailed covariates, blocking arguments, and martingale concentration for input-dependent noise. We then apply these tools to obtain finite-sample learning guarantees for fully observed bilinear systems, partially observed bilinear systems, and linear systems with bilinear observations. For control, we discuss quadratic control from bilinear observations, where the classical separation principle fails, and review tractable approaches based on belief-space receding horizon control. We also cover stabilization of bilinear dynamics under state feedback using semi-definite programming, LMI relaxations, sum-of-squares methods, and Koopman-based lifting. We conclude by discussing connections to reinforcement learning and machine learning, and some open problems in combined learning and control of bilinear systems.
Topics
Scope
- Least-squares theory for dependent and heavy-tailed covariates: one-sided Bernstein inequality, blocking arguments, martingale concentration
- Finite-sample identification of fully observed bilinear systems
- Finite-sample identification of partially observed bilinear systems and linear systems with bilinear observations
- Quadratic control from bilinear observations and the failure of the separation principle
- Dual control with belief-space receding horizon (model predictive) control
- Stabilization of bilinear dynamics: SDP, LMI relaxations, sum-of-squares, and Koopman-based lifting
- Open problems in combined learning and control of bilinear systems
Speakers
Speakers
Program
Session structure
Thursday, December 17, 2026 · 15:45–17:30 (Hawaii time), Room Coral 3-5, Hilton Hawaiian Village, Honolulu, Hawaii. Session ThCCT21 in the official CDC 2026 program.
| Time | Program |
|---|---|
| Introduction | |
| 15:45–15:55 | Sarah Dean / Maryam Fazel Learning and Control Beyond Linearity: Towards a Non-Asymptotic Theory for Bilinear Systems Summary · ThCCT21.1This opening talk sets the stage for the tutorial by introducing bilinear dynamics and observations through motivating examples. We explain the key challenges in bilinear learning and control; and outline the progression from statistical tools to end-to-end learning and control. |
| Part I – Learning: Non-asymptotic Bilinear System Identification | |
| 15:55–16:15 | Yassir Jedra Least-Squares Theory Revisited: Dependence Structures, Martingales and Heavy-Tailed Covariates Summary · ThCCT21.2Building on these challenges, this talk develops statistical tools for least-squares estimation with nonlinear, dependent, and heavy-tailed features. We then introduce statistical tools to establish persistence of excitation with heavy-tailed covariates; and to control truncation and input-dependent noise, providing the foundation for the identification results in the next talk. |
| 16:15–16:35 | Yahya Sattar Non-Asymptotic Bilinear System Identification: Bilinear Dynamics and Bilinear Observations Summary · ThCCT21.3Applying the preceding statistical tools, this talk establishes finite-sample identification guarantees from a single trajectory for fully and partially observed bilinear dynamics and linear dynamics with bilinear observations. We explain how input choice, stability, multi-step excitation, noise, truncation etc., affect estimation, preparing the transition from bilinear system identification to controller design. |
| 16:35–16:40 | Break |
| Part II – Control: Bilinear Dynamics, and Bilinear Observations | |
| 16:40–17:00 | Sarah Dean Control with Bilinear Observations: Sub-Optimality of the Separation Principle; Dual Control with Belief Space MPC Summary · ThCCT21.4Moving from identification to control, this talk examines bilinear observations, where control inputs affect both state evolution and information. We explain why the separation principle fail and certainty-equivalent control can be sub-optimal. We then introduce a belief-space MPC to balance regulation and information gathering. |
| 17:00–17:15 | Yahya Sattar / Yassir Jedra Control of Bilinear Dynamics: Koopman Theoretic Approaches, LMI-Based Design, and SOS Controller Synthesis Summary · ThCCT21.5After examining bilinear observations, we turn to bilinear dynamics under state feedback. We review LMI and SOS methods for synthesizing stabilizing controllers and certifying regions of attraction under model uncertainty, connecting identification errors to control guarantees. We then show how Koopman lifting extends these approaches to nonlinear systems while accounting for approximation errors. |
| Part III – Conclusions & Discussions | |
| 17:15–17:25 | Maryam Fazel / Sarah Dean End-to-End Learning and Control of Bilinear Systems Summary · ThCCT21.6Bringing together the preceding identification and control methods, this concluding talk considers end-to-end learning and control of bilinear systems. Finally, we discuss the connections to policy optimization, representation learning, and predictive world models for extending the tutorial’s results. |
| 17:25–17:30 | Questions |
Organizers
Session chairs
Organizers
Contact
Tutorial information
Session ThCCT21 at CDC 2026: Thursday, December 17, 2026 · 15:45–17:30 (Hawaii time), Room Coral 3-5, Hilton Hawaiian Village, Honolulu, Hawaii. For questions, contact ysattar@cornell.edu.