Consensus of multi-agent systems with unknown control directions by uniting dynamic and switching adaptive feedback

This paper investigates the asymptotic consensus for a class of uncertain multi-agent systems (MASs). The considered systems are affected by the unknown and nonidentical input coefficients whose unknown signs are called unknown control directions. Notably, "unknown" and "nonidentical" ingredients directly lead to the existence of the uncertainties and heterogeneities of the MASs, for which, a new consensus protocol is proposed by uniting switching scheme and continuous adaptive one. In the uniting strategy, the unknown signs of the input coefficients are estimated by the discontinuous switching scheme while the unknown values are compensated by the continuous adaptive scheme. Though Nussbaum-type gain function (continuous adaptive strategy) and traditional switching method (discontinuous strategy), have been verified to be solely effective for solving the problem considered in the paper, large control gains or terrible transient performances arguably exist. The paper intends to avoid the disadvantages of existing methods to some extend and unite them to develop a more effective uniting strategy for achieving consensus. Compared with the existing results, the protocol proposed in the paper guarantees that asymptotic consensus is achieved faster with smaller control gains, that is, better transient and steady state performances are pursued. The superiority of the developed uniting strategies in performance improving can be seen intuitively from the illustrative examples by simulation.