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Existing Nussbaum function based methods on the consensus of multi-agentsystems require (partial) identical unknown control directions of all agentsand cause dangerous dramatic control shocks. This paper develops a novelsaturated Nussbaum function to relax such limitations and proposes a Nussbaumfunction based control scheme for the consensus problem of multi-agent systemswith arbitrary non-identical unknown control directions and safe controlprogress. First, a novel type of the Nussbaum function with differentfrequencies is proposed in the form of saturated time-elongation functions,which provides a more smooth and safer transient performance of the controlprogress. Furthermore, the novel Nussbaum function is employed to designdistributed adaptive control algorithms for linearly parameterized multi-agentsystems to achieve average consensus cooperatively without dramatic controlshocks. Then, under the undirected connected communication topology, all thesignals of the closed-loop systems are proved to be bounded and asymptoticallyconvergent. Finally, two comparative numerical simulation examples are carriedout to verify the effectiveness and the superiority of the proposed approachwith smaller control shock amplitudes than traditional Nussbaum methods.

Novel Nussbaum-Type Function based Safe Adaptive Distributed Consensus Control with Arbitrary Unknown Control Direction