K-filter-based distributed adaptive bipartite tracking for nonlinear multi-agent systems with unknown control direction

This paper investigates K-filter-based distributed adaptive output-feedback bipartite tracking problem for multi-agent systems with unknown control direction. The agents are partitioned into two groups, where agents belonging to the same group are cooperative while agents belonging to the distinct group are competitive. Firstly, the unmeasurable state variables of the system under unknown control direction are estimated through K-filters. Then, a neighbourhood error is introduced to transform a structurally balanced network into a cooperative network. Based on K-filters, neighbourhood error, Nussbaum-type functions and dynamic surface control, a distributed adaptive output-feedback control protocol is designed to achieve the bipartite tracking. It is shown that all signals in the resulting closed-loop systems are semi-global bounded and the output of each agent can track the reference signal provided that the network is structurally balanced and contains a directed spanning tree. Finally, a numerical example is given to verify the effectiveness of the proposed method.