Adaptive consensus of second‐order nonlinear MASs with aperiodically time‐varying parameters and unknown control directions

The problem of adaptive consensus is addressed for a class of second‐order nonlinear multi‐agent systems with aperiodically time‐varying parameters and unknown control directions. Firstly, a new adaptive control approach, so‐called congelation of variables method, is adopted to deal with aperiodically time‐varying parameters which are fast‐varying in an unknown compact set with only their radii known a priori. Secondly, a novel Nussbaum‐type function approach is utilized to address the problem of unknown control directions. It is noteworthy that the control directions investigated in this paper are allowed to be completely unknown and nonidentical, whereas the unknown control directions in the most existing works are assumed to be identical. Thirdly, the unknown nonlinear function in each follower's dynamics is approximated by radial basis function neural network approximation technique. The approximation error, external disturbance in the follower's dynamics, as well as the leader's unknown acceleration dynamics are suppressed as an adaptive robust term, which can alleviate the online computational burden. Then, by designing time‐varying control gains updated adaptively with only local information, a fully distributed adaptive consensus control scheme is designed to guarantee that the multi‐agent systems achieve consensus asymptotically in the presence of unknown aperiodically time‐varying parameters, unknown nonidentical control directions, unknown nonlinearities, and external disturbances. Two simulation examples are provided to validate the effectiveness of the proposed consensus protocol.