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Control theory: mathematical perspectives on complex networked systems. Abstracts from the workshop held February 26 – March 3, 2012. (English) Zbl 1349.00031

Summary: Control theory is an interdisciplinary field that is located at the crossroads of pure and applied mathematics with systems engineering and the sciences. Its range of applicability and its techniques evolve rapidly with new developments in communication systems and electronic data processing. Thus, in recent years networked control systems emerged as a new fundamental topic, which combines complex communication structures with classical control methods and requires new mathematical methods. A substantial number of contributions to this workshop was devoted to the control of networks of systems. This was complemented by a series of lectures on other current topics like fundamentals of nonlinear control systems, model reduction and identification, algorithmic aspects in control, as well as open problems in control.

MSC:

00B05 Collections of abstracts of lectures
00B25 Proceedings of conferences of miscellaneous specific interest
93-06 Proceedings, conferences, collections, etc. pertaining to systems and control theory
37-06 Proceedings, conferences, collections, etc. pertaining to dynamical systems and ergodic theory
37N35 Dynamical systems in control
90Bxx Operations research and management science
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[1] D. Angeli, P. de Leenheer, and E.D. Sontag, ”Graph-theoretic characterizations of monotonicity of chemical networks in reaction coordinates”, J. Mathematical Biology, 61, (2010), 668Oberwolfach Report 12/2012 A stochastic approach to control of refrigerator appliances for frequency regulation David Angeli (joint work with A. Kountouriotis) Dynamic demand management is a promising research direction for improving power system resilience. In a power network, the system frequency (mains frequency) can be interpreted as a measure of the balance between demand (load) and supply (generation), with perfect balance corresponding to the nominal value of 50Hz. In cases where demand exceeds the available supply, the frequency drops below 50Hz, while excess supply leads to frequency rising above 50Hz. As a result, system frequency continuously fluctuates around the nominal level, and the system operator ensures that the balance between demand and supply is continuously maintained, stabilizing the frequency within narrow bands around 50Hz, by regulating the available supply. In order for such (supply) regulation to be possible, however, it is required that ’frequency response services’, as well as sufficient reserves, are included in the system This is essential not only for instantaneous frequency balancing, but, more importantly, for the ability to respond to sudden power plant failures, which would otherwise lead to severe blackouts. These ’support’ services, however, significantly add to the cost of power generation, and any method which manages to reduce the magnitude of these services, without sacrificing system stability, is of significant importance. ”Dynamic demand control” is a recent research direction, which focuses on the possibility of using frequency responsive loads, so as to reduce the amount of frequency response and reserve services that are required. In this poster, we consider the problem of managing power demand by means of ”smart” thermostatic control of domestic refrigerators. In this approach, the operating temperature of these appliances, and thus their energy consumption, is modified dynamically, within a safe range, in response to mains frequency fluctuations. An individual refrigerator is represented as a hybrid automaton, capable of switching between 2 states (an ON state and an OFF states). Simple affine first order equations are assumed to describe the evolution of the temperature within the two states: T = (T TON)T = (T TOF F) where {\(\alpha\)} is a coefficient which characterizes the thermal dispersion of the refrigerator, TOF Fis the ambient temperature, and TONis the temperature that the refrigerator would reach asymptotically if always ON. In order to compensate for frequency fluctuations dynamically we define a stochastic and frequency dependent switching policy. In particular, individual refrigerators adopt a Markovian switching policy (that is they behave as stochastic Control Theory: Mathematical Perspectives on Complex Networked Systems 669
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