Distributed Adaptive Resource Allocation
An Uncertain Saddle-Point Dynamics Viewpoint
Dongdong Yue (Southeast University)
Simone Baldi (Southeast University)
Jinde Cao (Yonsei University, Southeast University)
Qi Li (Southeast University)
Bart De Schutter (TU Delft - Delft Center for Systems and Control)
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Abstract
This paper addresses distributed adaptive optimal resource allocation problems over weight-balanced digraphs. By leveraging state-of-the-art adaptive coupling designs for multiagent systems, two adaptive algorithms are proposed, namely a directed-spanning-tree-based algorithm and a node-based algorithm. The benefits of these algorithms are that they require neither sufficiently small or unitary step sizes, nor global knowledge of Laplacian eigenvalues, which are widely required in the literature. It is shown that both algorithms belong to a class of uncertain saddle-point dynamics, which can be tackled by repeatedly adopting the Peter-Paul inequality in the framework of Lyapunov theory. Thanks to this new viewpoint, global asymptotic convergence of both algorithms can be proven in a unified way. The effectiveness of the proposed algorithms is validated through numerical simulations and case studies in IEEE 30-bus and 118-bus power systems.