Distributed Adaptive Time-Varying Group Formation Tracking for Multi-Agent Systems with Multiple Leaders on Directed Graphs

This paper proposes a fully-distributed control protocol that achieves time-varying group formation tracking for linear multi-agent systems connected via directed graph. The group formation tracking often leads to sub-formations especially when the leaders are placed far apart or they have separate control inputs. In the proposed approach, the followers are distributed into several subgroups and each subgroup attains the predefined sub-formation along with encompassing the leaders. Each subgroup can be assigned multiple leaders, contrary to the single-leader case considered in most of the existing literature, which makes the current problem non-trivial. When multiple leaders exist in a subgroup, the sub-formation attained by that subgroup keeps tracking a convex combination of the states of the leaders. A distributed adaptive control protocol has been introduced in this paper which uses only relative state information and thus avoids direct computation of the graph Laplacian matrix. Due to virtue of this, the proposed scheme remains effective even when some of the agents get disconnected from the network due to sudden communication failure. An algorithm is provided to outline the steps to design the control law to attain time-varying group formation tracking with multiple leaders. Towards the end, a case study on multi-target surveillance operation is taken up to show an important application of the proposed adaptive control technique.