Abstract
In this work, we propose a new framework for solving the optimal consensus problem of agents with continuous dynamics. Motivated by the EXTRA algorithm, we introduce novel auxiliary continuous variables that utilize only sampled measurements of the neighbor outputs. The use of suitable smoothing functions, which allow us to gradually incorporate the samples in the new variables within a sampling period, guarantees the continuity of these variables. It is shown that the regulation of these EXTRA-based Smoothed Optimal Consensus (EXTRA-SOC) variables to a neighborhood of zero ensures approximate optimal consensus of the agent outputs. Taking this property into account, adaptive fuzzy distributed controllers are then designed for fully actuated Lagrangian agents that approximate the unknown system nonlinearities and guarantee approximate optimal consensus of all agent outputs. Moreover, all closed-loop signals are proven to remain bounded. Simulations on a swarm of wheeled robots validate the effectiveness of the proposed approach.
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