From Covariance Steering to Multimodal Density Steering: Theory and Applications

Abstract

Covariance steering provides a systematic framework for controlling the mean and covariance of uncertain dynamical systems. However, controlling only the first two moments may be insufficient when the objective is to steer more complex, potentially multimodal state distributions. This talk presents a framework for steering Gaussian mixture models (GMMs) through randomized control policies constructed from Gaussian-to-Gaussian covariance steering laws. We discuss how this approach leads to a linear programming formulation for steering between prescribed GMMs and bilinear optimization formulations for problems involving terminal distribution matching and constraints on expected control performance. Computational solution methods based on block-coordinate descent are also presented. Finally, we illustrate the proposed multimodal density steering framework through applications to multi-agent coverage and shape control of deformable structures.

Biography

Dr. Bakolas is a Professor in the Department of Aerospace Engineering and Engineering Mechanics at The University of Texas at Austin which he joined as an Assistant Professor in fall 2012. He received his Diploma in Mechanical Engineering with highest honors from the National Technical University of Athens, Greece, in 2004 and his MS. and Ph.D. degrees in Aerospace Engineering from the Georgia Institute of Technology, Atlanta, in 2007 and 2011, respectively. He is an Associate Fellow of AIAA and a Senior Member of IEEE. He serves as a Senior Editor for the Guidance and Control technical track of IEEE Transactions on Aerospace and Electronic Systems.

His research is mainly focused on optimal control theory, control of uncertain systems, data-driven control of complex systems (e.g., fluid flows), differential games, and control of multi-agent systems. Other interests include optimal decision-making, nonlinear control theory, path/motion planning, and optimization-based control.