Oberwolfach Reports

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Volume 12, Issue 1, 2015, pp. 597–659
DOI: 10.4171/OWR/2015/12

Control Theory: A Mathematical Perspective on Cyber-Physical Systems

Frank Allgöwer[1], Uwe Helmke[2] and Naomi Leonard[3]

(1) Institut für Systemtheorie technischer Prozesse, Universität Stuttgart, Pfaffenwaldring 9, 70550, Stuttgart, Germany
(2) Mathematisches Institut, Universität Würzburg, Am Hubland, 97074, Würzburg, Germany
(3) Department of Mechanical and Aerospace Engineering , Princeton University, D-234 Engineering Quadrangle, NJ 08544, Princeton, USA

Control theory is an interdisciplinary field that is located at the crossroads of pure and applied mathematics with systems engineering and the sciences. Recently the control field is facing new challenges motivated by application domains that involve networks of systems. Examples are interacting robots, networks of autonomous cars or the smart grid. In order to address the new challenges posed by these application disciplines, the special focus of this workshop has been on the currently very active field of Cyber-Physical Systems, which forms the underlying basis for many network control applications. A series of lectures in this workshop was devoted to give an overview on current theoretical developments in Cyber-Physical Systems, emphasizing in particular the mathematical aspects of the field. Special focus was on the dynamics and control of networks of systems, distributed optimization and formation control, fundamentals of nonlinear interconnected systems, as well as open problems in control.

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Allgöwer Frank, Helmke Uwe, Leonard Naomi: Control Theory: A Mathematical Perspective on Cyber-Physical Systems. Oberwolfach Rep. 12 (2015), 597-659. doi: 10.4171/OWR/2015/12