Data-Driven Dynamic Ambiguity Sets: Precision Tradeoffs under Noisy Measurements

ABSTRACT: Stochastic and robust optimization constitute natural frameworks to solve decision-making and control problems subject to uncertainty. However, these fall short in addressing real-world scenarios for which models of the uncertainty are not available. Data-driven approaches can be of help to approximate such models, but typically require large amounts of data in order to produce performance-guaranteed results. Motivated by settings where the collection of data is costly and fast decisions need to be made online, we present recent work on the construction of dynamic ambiguity sets for uncertainties that evolves according to a dynamical law. In particular, we characterize the tradeoffs between the amount of progressively assimilated data and its future adequacy, due to its gradual precision loss in its predicted values.

BIO: Sonia Martínez is a Full Professor at the Department of Mechanical and Aerospace Engineering at the University of California, San Diego and a Jacobs Faculty Scholar. Prof. Martínez received her Ph.D. degree in Engineering Mathematics from the Universidad Carlos III de Madrid, Spain, in May 2002. Following a year as a Visiting Assistant Professor of Applied Mathematics at the Technical University of Catalonia, Spain, she obtained a Postdoctoral Fulbright Fellowship and held appointments at the Coordinated Science Laboratory of the University of Illinois, Urbana-Champaign during 2004, and at the Center for Control, Dynamical systems and Computation (CCDC) of the University of California, Santa Barbara during 2005. From January 2006 to June 2010, she was an Assistant Professor with the department of Mechanical and Aerospace Engineering at the University of California, San Diego. From July 2010 to June 2014, she was an Associate Professor with the department of Mechanical and Aerospace Engineering at the University of California, San Diego.

Dr Martínez’ research interests include networked control systems, multi-agent systems, and nonlinear control theory with applications to robotics and cyber-physical systems. In particular, she has focused on the modeling and control of robotic sensor networks, the development of distributed coordination algorithms for groups of autonomous vehicles, and the geometric control of mechanical systems. For her work on the control of underactuated mechanical systems she received the Best Student Paper award at the 2002 IEEE Conference on Decision and Control. She was the recipient of a NSF CAREER Award in 2007. For the co-authored papers “Motion coordination with Distributed Information,” and “Tutorial on dynamic average consensus: The problem, its applications, and the algorithms”, she received, respectively, the 2008 and 2021 Control Systems Magazine Outstanding Paper Award. She is a Senior Editor of Automatica and an IEEE Fellow. Recently, she was named the inaugural Editor in Chief of a new Control System Society publication, the IEEE Open Journal of Control Systems (IEEE OJ-CSYS).

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