Adaptive Coordination of Networked Lagrangian Systems With Nonsmooth Actuator Nonlinearities

In this article, we present a solution to the adaptive coordination control problem for networked Lagrange systems with unknown nonsmooth actuator nonlinearities, which can represent actuator failure/attack, deadzone, backlash, friction, and hysteresis in a unified framework. An auxiliary system is firstly designed for each subsystem over a directed network, in which the final synchronized value can be regulated by given specified initial values. Then, an adaptive controller is proposed for networked Lagrangian systems using an adaptive dynamic gain approach. Asymptotical stability is established by using the Lyapunov direct method. Compared to the adaptive regression approach, the nonsmooth actuator dynamics is not required to be known and the synchronized value can be arbitrarily designed. Finally, simulation results are presented to verify the proposed approach.