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Time-delay phenomena extensively exist in practical systems, e.g., multi-agent systems, bringing negative impacts on their stabilities. This work analyzes a collaborative control problem of redundant manipulators with time delays and proposes a time-delayed and distributed neural dynamics scheme. Under assumptions that the network topology is fixed and connected and the existing maximal time delay is no more than a threshold value, it is proved that all manipulators in the distributed network are able to reach a desired motion. The proposed distributed scheme with time delays considered is converted into a time-variant optimization problem, and a neural dynamics solver is designed to solve it online. Then, the proposed neural dynamics solver is proved to be stable, convergent and robust. Additionally, the allowable threshold value of time delay that ensures the proposed scheme's stability is calculated. Illustrative examples and comparisons are provided to intuitively prove the validity of the proposed neural dynamics scheme and solver.
Jin et al. (Tue,) studied this question.