W8: Control of Distributions: Theory and Applications (0126)

Efstathios Bakolas, Yongxin Chen, Abhishek Halder, Panagiotis Tsiotras

Date & Time



Feedback control has been ubiquitous because it can deal with uncertainty and improve system performance. However, traditionally, feedback has been used to control uncertainty in a rather indirect manner. Directly controlling the effect of uncertainty on a dynamical system implies the direct control of the future evolution of the distribution of the system trajectories, an infinite-dimensional, and often intractable problem. However, several recent advances have made it possible to control second and higher order moments of these trajectory distributions in a systematic and precise manner. This workshop will bring together several researchers working in the area of distributional control in order to promote the interchange of the latest ideas, and demonstrate how the theory can be applied in a variety of applications of interest to engineers and scientists.

Control of distributions, or population of states, arise across applications ranging from decentralized shaping of swarms, stochastic motion planning, and regulating neuronal ensembles for biomedical purposes. This is an emergent research direction in systems-control engineering situated at the confluence of contemporary topics in statistical physics and machine learning, such as the optimal mass transport and the Schrödinger bridge. While the latter topics have long histories, that they can be seen as particular instances of certain class of stochastic optimal control problems, is a rather recent realization. This class of stochastic optimal control problems asks for direct controller synthesis to steer distributions in the state space, and is atypical with respect to control literature in the following sense: classical stochastic optimal control focused on “control with uncertainties” while this new class calls for “control of uncertainties”. From this perspective, the recent theoretical and algorithmic strides made for the control of distributions, push the frontiers of stochastic control. With this context in mind, the proposed workshop is a timely effort to apprise the systems-control community about the current progress in this fast moving research field, and to catalyze the current research momentum to further the theory and applications in this area.

The proposed workshop will strike a balance between the theory and applications of distributional control. Its main goal is to bring together researchers across systems control engineering to inform about recent advances, put the different strands of progress in perspective to get a clearer view of the research landscape, and promote discussions and collaborations to pursue the exciting vistas ahead. Several topics that reflect the main philosophy behind controlling distributions will be discussed and summarized. In addition to the nine planned talks delivered by leading researchers in distributional control, the dedicated Q&A session in the afternoon will allow all participants to engage in lively discussions.

Target Audience: includes graduate students and researchers in control, robotics, machine learning, physicists and engineers working on the modeling and control of uncertain systems. The topics covered in this workshop will be particularly useful to students and researchers working on stochastic optimal control, stochastic model predictive control, and trajectory optimization problems for uncertain systems (e.g., autonomous robotic systems operating in dynamic environments The invited talks of this workshop will also be of interest to researchers working on uncertainty quantification and, in particular, its various applications to uncertain dynamical systems. The topics covered in this workshop will provide these researchers with unique insights into the ways that uncertainty and noise impact the propagation of the state distributions of subject to the trajectory-level dynamics.

Suggested Prerequisites: a basic knowledge of multivariable control of the depth covered in a standard graduate level class will be sufficient. Some familiarity with the stochastic differential equations would be beneficial, but not necessary. Finally, knowledge of the basic concepts and algorithmic tools from convex optimization and the theory of optimal mass transport would also be useful to better understand some of the proposed solution approaches for the control of distributions.


Opening Remarks

Session 1: Aerospace and Robotics Applications

  • Covariance Steering as a Tool for Planning in the Presence of Uncertainty
  • Koopman Operator Approach to Optimal Control and Chance-Constrained Motion Planning
  • for Systems with Parameter Uncertainty
  • Distributional Control: From Robotics to Applied Physics and Backwards

Coffee Break

Session 2: Swarms and Ensemble Control

  • Decentralized Control of Multi-Agent Systems using Local Density Feedback
  • Moment-Based Ensemble Control using Aggregated Measurements

Lunch Break

Session 3: Data-Driven Design of Population Observers and Controllers

  • Sample-based Population Observers
  • Real-time Trajectory Generation
  • Algorithms for Uncertain Dynamical Systems Using Covariance Steering

Coffee Break

Session 4: Nonlinear Regulation and Interpolation

  • Finite Horizon Optimal Density Regulation for Nonlinear Systems
  • Wasserstein Spline: Theory and Applications

Q&A and Discussions

Closing Remarks and Adjourn


Efstathios Bakolas

Department of Aerospace Engineering and Engineering Mechanics, The University of Texas at Austin, Austin, TX

Yongxin Chen

School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA

Abhishek Halder

Department of Applied Mathematics, University of California, Santa Cruz, CA

Panagiotis Tsiotras

School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA

Date & Time