Distributed adaptive affine formation control for heterogeneous linear networked systems

This paper addresses the distributed adaptive affine formation protocol design problem for the heterogeneous leader-follower-type linear networked systems, in which the interaction graph is directed. Compared with the existing methods, the affine formation control has the superiority to tackle the motion constraints of the target formation based on the affine transformation in the arbitrary dimensional space. This transformation has the property of acting as a linear transformation, and the complexity of formation controllers can be reduced. Only the partial information of the graph can be acquired by the agents, and the adaptive algorithms are adopted to find the corresponding bounds of the control gains. By introducing the additive functions for both proportional and integral terms, a distributed adaptive proportional-integral-type control algorithm of achieving the affine formation is presented. This distributed control scheme can eliminate the steady-state errors based only on the relative states of neighboring agents. The corresponding numerical simulations are carried out to verify the theoretical results; numerous types of formation patterns can be obtained.