Robust leaderless time-varying formation control for unmanned aerial vehicle swarm system with Lipschitz nonlinear dynamics and directed switching topologies

This paper tackles the robust leaderless Time-Varying Formation (TVF) control problem for the Unmanned Aerial Vehicle (UAV) swarm system with Lipschitz nonlinear dynamics, external disturbances and directed switching topologies. In comparison with the previous achievements on formation control problems, the UAV swarm system with Lipschitz nonlinear dynamics can accomplish the pre-designed TVF while tracking a pre-given trajectory which is produced by a virtual leader UAV in the presence of external disturbances. Firstly, by applying the consensus theory, a TVF controller is developed with the local neighborhood status information, the errors of real time status of all UAVs, the expected formation configuration and the pre-given trajectory under directed switching topologies. Secondly, through a certain matrix variable substitution, the UAV swarm system formation control issue is transformed into a lower dimensional asymptotically stable control issue. Thirdly, by introducing the minimum dwell time, the design steps of formation control algorithm are further acquired. In the meantime, the stability of the UAV swarm system is analyzed through the construction of a piecewise continuous Lyapunov functional and via the Linear Matrix Inequalities (LMIs) method. Finally, the comparison results of a numerical simulation are elaborated to verify the validity of the proposed approach.