Distributed robust adaptive formation control of multi-agent systems with heterogeneous uncertainties and directed graphs

This paper studies distributed time-varying formation control problems for a class of linear systems with heterogeneous uncertainties and directed graphs. Both the cases without and with an active leader having unknown control inputs are considered. Two new robust adaptive formation protocols are designed in a totally distributed fashion, both of which incorporate two parts: a fully distributed nominal controller relying on the neighbors' relative state information and an adaptive compensating signal to restrain the influences of uncertainties. An original adaptive compensating strategy is proposed herein to deal with uncertainties related to not only system states but also control inputs. On the basis of adaptive mechanism, the controller design requires neither global information about communication topologies nor the upper bounds of uncertainties and the leader's control inputs. Based on Lyapunov arguments, sufficient conditions to achieve the desired formation are derived in terms of Riccati equations. The proposed protocols guarantee that the formation errors can converge to zero. Finally, the theoretical results are demonstrated by numerical simulations.