Backstepping-based synchronisation of uncertain networked Lagrangian systems
Wenlin Zhang, Zheng xin Wang, Yi Peng Guo · International Journal of Systems Science · 2012
In this article, we study the synchronisation problem of uncertain networked Lagrangian systems on directed communication topologies. For the nominal model without uncertainties, we propose a backstepping-based synchronisation design for heterogenous Lagrangian systems on directed graphs with a spanning tree. We relax earlier constraints on the feedback gain for the distributed synchronisation control law, which encompasses the existing double integrator consensus problem as a special case. We then extend the proposed design to the case without relative velocity measurement. For the uncertain Lagrangian model, we develop a distributed adaptive redesign so that asymptotic synchronisation convergence is achieved in the presence of linearly parameterised model uncertainties. Simulation results show the effectiveness of the proposed method.