This paper considers the design of a distributed dual-mode extremum seeking control (a proportional-integral extremum seeking control) technique for addressing equality constrained resource allocation problems of multi-agent systems in real-time. We address problems where the structure of each agent's resource allocation function is unknown but depends on the entire resource allocation vector. We incorporate dynamics and tackle this problem for a dynamic system. A cooperative approach that permits communication between neighboring agents to minimize the unknown overall resource allocation function subject to the resource requirement is utilized. A simulation example is included to show the effectiveness of the proposed technique.
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