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Existing Nussbaum function based results on consensus of multi-agent systems require that the unknown control directions of all the agents should be the same. This note proposes an adaptive method to relax such a requirement to allow non-identical control directions, under the condition that some control directions are known. Technically, a novel idea is proposed to construct a new Nussbaum function, from which a conditional inequality is developed to handle time-varying input gains. Then, the inequality is integrated with adaptive control technique such that the proposed Nussbaum function for each agent is adaptively updated. Moreover, in addition to parametric uncertainties, each agent has non-parametric bounded modelling errors which may include external disturbances and approximation errors of static input nonlinearities. Even in the presence of such uncertainties, the proposed control scheme is still able to ensure the states of all the agents asymptotically reach perfect consensus. Finally, simulation study is performed to show the effectiveness of the proposed approach.
Chen et al. (Fri,) studied this question.
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