A review of distributed control of multi-agent systems with unknown control directions: a Nussbaum-function perspective

Distributed control of multi-agent systems (MASs) with unknown control directions (UCDs), where the signs of high-frequency gains are unknown a priori, has attracted significant research interest due to both theoretical significance and practical relevance. This survey reviews recent progress on distributed Nussbaum-function-based approaches. The discussion begins with first-order models, subsequently extending to second-order systems, higher-order nonlinear dynamics, and Euler-Lagrange systems. Furthermore, representative results concerning event-triggered communication and state-constrained consensus are examined. For each line of research, we summarise typical assumptions and technical requirements, including identical versus nonidentical control directions and undirected versus directed interaction topologies. Finally, several open challenges and promising directions for future investigation are outlined.