1,011 research outputs found
Controllability Issues of Linear Ensemble Systems
We address an open problem in ensemble control: Whether there exist
controllable linear ensemble systems over high dimensional parameterization
spaces? We provide a negative answer: Any real-analytic linear ensemble system
is not -controllable, for , if the dimension
of its parameterization space is greater than one
Structurally Robust Control of Complex Networks
Robust control theory has been successfully applied to numerous real-world
problems using a small set of devices called {\it controllers}. However, the
real systems represented by networks contain unreliable components and modern
robust control engineering has not addressed the problem of structural changes
on a large network. Here, we introduce the concept of structurally robust
control of complex networks and provide a concrete example using an algorithmic
framework that is widely applied in engineering. The developed analytical
tools, computer simulations and real network analyses lead herein to the
discovery that robust control can be achieved in scale-free networks with
exactly the same order of controllers required in a standard non-robust
configuration by adjusting only the minimum degree. The presented methodology
also addresses the probabilistic failure of links in real systems, such as
neural synaptic unreliability in {\it C. elegans}, and suggests a new direction
to pursue in studies of complex networks in which control theory has a role.Comment: 36 pages, 22 figures. This paper was submitted to a journal in May
2014 and still under review. Please cite the arxiv version if your work is
related to our researc
Control Theory: A Mathematical Perspective on Cyber-Physical Systems
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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