Robust synchronisation tracking control of networked Euler–Lagrange systems using reference trajectory estimation based on virtual double-integrators

Abstract

This paper considers the problem of distributed synchronisation tracking control of multiple Euler–Lagrange systems on a directed graph which contains a spanning tree with the leader node being the root. To design the high performance distributed controllers, a virtual double-integrator is introduced in each agent and is controlled by a virtual distributed linear high-gain synchronisation tracking controller, so that the position and velocity of each agent track those of the reference trajectory with arbitrarily short transient time and small ultimate tracking error. Then taking the double-integrator's position and velocity as the estimates of those of the reference trajectory, in each generalised coordinate of each Euler–Lagrange agent, a local controller with a disturbance observer and a sliding mode control term is designed, to suppress the mutual interactions among the agents and the modelling uncertainties. The boundedness of the overall signals and the synchronisation tracking control performance are analysed, and the conditions for guaranteed control performance are clarified. Simulation examples are provided to demonstrate the performance of the distributed controllers.

Keywords:

• Euler–Lagrange systems
• distributed control
• synchronisation tracking
• direct graph
• high-gain observer
• disturbance observer
• sliding mode control