Fractional PID consensus control protocols for second-order multiagent systems

Document Type

Conference Proceeding

Publication Date



Engineering Technology

Publication Title

AIAA Scitech 2019 Forum


We outline the formalism and investigate the efficacy of fractional PIDα consensus control for second-order multiagent systems in which the derivative feedback is allowed to take non-integer order. Using algebraic graph theory to characterize the communication topology, a pseudostate-space formalism is developed in terms of the graph Laplacian matrix and used to prove that, given certain conditions on the system’s eigenvalues, consensus is guaranteed to be reached asymptotically. We show that these eigenvalue conditions correspond to particular regions of {kP, kI, kD, αD} parameter space and demonstrate this numerically as well as analytically for the special case of a complete graph. Finally, we show that fractional-order controllers outperform standard integer-order controllers in terms of common performance specifications for a selection of benchmark 5-agent systems.

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