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Topics in data-driven control
In a typical control design problem, the role of data has been long dictated by indirect approaches, where system identification is sequentially followed by model-based control. However, the advent of large data sets and the ever-increasing computing power, combined with the ongoing revolution brought about by machine learning technologies, has recently triggered a renewed appreciation for direct approaches, where the objective is to infer optimal decisions directly from measured data. The new wave of data-driven control algorithms has primarily modeled uncertainty by ellipsoids. While effective in many circumstances, this approach disregards the geometric structure of the data, leading to possibly coarse characterizations of uncertainty. This project explores the problem of uncertainty quantification by regarding system behaviors as subspaces of fixed dimension (represented by data matrices) and exploiting the underlying Grassmannian geometry.
See .pdf for more detail.
Keywords: data-driven control, differential geometry, numerical linear algebra.
The purpose of this thesis is quite malleable. For practically oriented students, the focus will be on applying and evaluating new data-driven control algorithms on problems arising in the field of robotics. For theoretically oriented students, the focus will be on studying and possibly developing new uncertainty quantification metrics, leveraging on behavioral system theory as well as advanced tools from optimization, differential geometry and numerical linear algebra.
The purpose of this thesis is quite malleable. For practically oriented students, the focus will be on applying and evaluating new data-driven control algorithms on problems arising in the field of robotics. For theoretically oriented students, the focus will be on studying and possibly developing new uncertainty quantification metrics, leveraging on behavioral system theory as well as advanced tools from optimization, differential geometry and numerical linear algebra.
The student will: (1) learn and understand concepts related to the topic, including behavioral system theory and data-driven predictive control; (2) explore and review the relevant literature; (3) study a problem statement with potential applications arising from robotics; (4) evaluate the performance of the proposed methodology using and developing data-driven control software tools in Matlab or Python.
Prerequisites: The project is well suited for a student who enjoys numerical mathematics. A background in analysis and linear algebra is required. Knowledge of optimization, differential geometry and numerical linear algebra is also beneficial.
The student will: (1) learn and understand concepts related to the topic, including behavioral system theory and data-driven predictive control; (2) explore and review the relevant literature; (3) study a problem statement with potential applications arising from robotics; (4) evaluate the performance of the proposed methodology using and developing data-driven control software tools in Matlab or Python.
Prerequisites: The project is well suited for a student who enjoys numerical mathematics. A background in analysis and linear algebra is required. Knowledge of optimization, differential geometry and numerical linear algebra is also beneficial.
Jeremy Coulson - Email: jcoulson@ethz.ch
Dr. Alberto Padoan - Email: apadoan@ethz.ch
Jeremy Coulson - Email: jcoulson@ethz.ch Dr. Alberto Padoan - Email: apadoan@ethz.ch