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**1 - 1**of**1**### Using Fractional-Order Differential Equations for Health Monitoring of a System of Cooperating Robots*

"... Abstract—The dynamics of many large-scale robotic forma-tion systems, including structured systems as well as some ran-dom scale-free networks of agents, can be accurately described using fractional-order differential equations. A fractional-order differential equation can contain derivative terms w ..."

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Abstract—The dynamics of many large-scale robotic forma-tion systems, including structured systems as well as some ran-dom scale-free networks of agents, can be accurately described using fractional-order differential equations. A fractional-order differential equation can contain derivative terms with non-integer order, e.g., the one-half derivative. This paper demon-strates 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. Integer-order 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