Distributed adaptive leader-following consensus control of connected Lagrangian systems with input hysteresis quantization and time-varying control gain

Abstract This paper studies two cases of leader-following consensus problems for a class of connected Lagrangian systems, which include input quantization, time-varying control gain and unknown bounded external disturbance under undirected and directed communication topologies. Because it is usually not easy to correctly measure the upper bounds of time-varying control gain, nor to measure bounded external disturbance, the upper bounds are considered unknown in this paper. In the undirected communication graph case, the bound of the leader’s trajectory can be estimated by a group of observers for each agent. Then, based on the new technique of two-step adaptive distributed control, the tracking errors can asymptotically converge to zero. In the directed communication graph case, only the neighbors’ position and velocity information are needed for the control protocol design, and the two-step adaptive method is used. The tracking errors in this case have the adjustable ultimate uniform boundedness. Moreover, the nonlinearities of the input quantization and the time-varying control gain can be compensated by a carefully selected smooth control protocol in both cases. It is shown that all the closed-loop signals are uniformly bounded, and a practical example simulation is given to demonstrate the effectiveness of the proposed scheme.