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FractionalOrder Dynamics in a Random, Approximately ScaleFree Network of Agents
"... Abstract—Differential equations with fractionalorder derivatives, e.g., the “onehalf ” derivative, have a long history in mathematics, but have not yet attained mainstream use in engineering and applied science. While applications do exist in modeling specific phenomena such as viscoelasticity a ..."
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Abstract—Differential equations with fractionalorder derivatives, e.g., the “onehalf ” derivative, have a long history in mathematics, but have not yet attained mainstream use in engineering and applied science. While applications do exist in modeling specific phenomena such as viscoelasticity and other types of difficulttomodel phenomena, and extensions to control such as in fractionalorder PID do exist, everyday use of fractional order modeling is uncommon. A subset of complex systems called CyberPhysical Systems (CPS) is receiving much emphasis in the research community. In this paper we show examples of networked system models which exhibit fractionalorder dynamic responses. This suggests that fractionalorder dynamics may be prevalent in CPS and hence may be an important and useful modeling tool in that area. We particularly focus on a scale free networked system. I.
Using FractionalOrder Differential Equations for Health Monitoring of a System of Cooperating Robots*
"... Abstract—The dynamics of many largescale robotic formation systems, including structured systems as well as some random scalefree networks of agents, can be accurately described using fractionalorder differential equations. A fractionalorder differential equation can contain derivative terms w ..."
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Abstract—The dynamics of many largescale robotic formation systems, including structured systems as well as some random scalefree networks of agents, can be accurately described using fractionalorder differential equations. A fractionalorder differential equation can contain derivative terms with noninteger order, e.g., the onehalf derivative. This paper demonstrates that the fractional order of the dynamics of a system may be a potentially powerful new way to monitor the operational status of such systems. When the order of the system changes, it can indicate an important change in the status of the system. Integerorder models will never exhibit a change in order because the order is dictated by a natural first principle and the structure of the system. For this reason, traditional health monitoring tools essentially focus on identifying parameter variations in a mathematical description of the system, but not