Time-varying output formation control for heterogeneous multi-agent systems under the signed graph

This paper studies time-varying output formation control for linear heterogeneous multi-agent systems (MASs) under signed graphs, employing an adaptive dynamic event-based approach. The signed graph framework is used to model agent interactions, encompassing both cooperative and antagonistic behaviours. Firstly, a data-driven learning algorithm is given for the estimation of the unknown leader system matrix. Secondly, for a single leader MAS, a distributed adaptive dynamic event-based bipartite compensator is designed to estimate the leader's state. This triggering function utilises the internal dynamic variable to dynamically adjust the threshold, ensuring fewer triggering instances compared to traditional static thresholds. Thirdly, a controller integrating the compensator and observer is developed to solve the time-varying output formation control problem for heterogeneous MASs with signed graphs under a single leader. Subsequently, the findings are extended to multi-leader MASs, providing a solution for the formation control problem in such scenarios. Finally, several illustrative examples are provided to validate the theoretical results.