Distributed Adaptive Formation Control for Linear Swarm Systems with Time-Varying Formation and Switching Topologies

In this paper, distributed time-varying formation (TVF) control problems for general linear swarm systems with switching interaction topologies are investigated using an adaptive dynamic protocol. First, a TVF control protocol for switching interaction topologies is constructed using the states of neighboring agents. In the protocol, an adaptive controller that employs gain scheduling technique is provided to estimate the coupling weights among agents. Compared with the previous studies on formation control, the desired formation can be specified by piecewise continuously time-varying differentiable vectors, the interaction topology can be switching, and the disadvantage of requiring global information of the interaction topologies is removed in this paper. Then, an algorithm including a feasible formation condition is proposed to determine the gain matrices of the distributed adaptive formation protocol by solving a linear matrix inequality for swarm systems with switching interaction topologies. Moreover, under the designed distributed adaptive formation protocol, sufficient condition for general linear swarm systems with switching interaction topologies to achieve the given TVF is derived using the Lyapunov theory. Finally, numerical simulations are presented to demonstrate the obtained results.