Distributed control of nonlinear systems with unknown time-varying control coefficients: A novel Nussbaum function approach

In this paper, distributed control of uncertain multi-agent systems (MAS) with completely unknown nonlinearities, unknown time-varying control coefficients and multiple unknown control directions is investigated. Firstly, a new theorem with a series of novel Nussbaum functions are presented, which solve the outstanding problem in control of nonlinear systems with unknown time-varying control coefficients and unknown signs. Secondly, global consensus of MAS with unknown time-varying control coefficients and unknown system nonlinearities under directed graph is firstly achieved, and the transient tracking performance is also guaranteed. Thirdly, a novel filter is proposed for each agent which does not require a prior knowledge of time derivative of leader. Finally, simulation results show the effectiveness of the proposed control schemes.