A Distributed Algorithm for Tracking General Functions of Multiple Signals Not-Necessarily Having Steady States

This brief exploits the possibility of devising an algorithm for tracking a general function pertaining to multiple signals from a multi-agent system in a distributed sense, where each agent has access to one single signal. Each agent's input relies solely on local neighboring information, from which some conditions on the gain parameters, the reference signals, along with the general function, are derived such that the tracking objective is attainable. The algorithm is well-defined as long as the gradient of the general function with respect to agents' states has a uniform lower bound. Under mild conditions, it is shown that the devised system is able to track a general consensus function of multiple dynamic signals, including arithmetic mean, geometric mean, and root-mean square as special examples. The effectiveness of the proposed algorithm is demonstrated via numerical examples.