Pulse-Modulated Sampled-Data Second-Order Consensus for Multiple Euler-Lagrange Systems Without Neighbors’ Velocity Measurement

This paper studies the sampled-data second-order consensus of multiple Euler-Lagrange systems without knowing neighbors’ velocities. The second-order feedback control method of the Euler-Lagrange system naturally excludes the infinities in the control input that arise alongside sampled-data communication. It also avoids the auxiliary variable, which is seen as a disturbance. However, the control input is still discontinuous at sampling instants and not attainable for most real-world applications. The main goal of this work is to design a relatively smooth control input for the second-order consensus of Euler-Lagrange systems. The pulse-modulated scheme is employed to smoothen the discontinuities caused by the sampled communication. Necessary and sufficient consensus conditions are established through discretization and stability theory. It is shown that the shape of the pulse function also influences consensus in addition to its integral. Finally, numerical examples show that the proposed pulse-modulated control scheme smoothens the control inputs and ensures consensus under the criterion.