Distributed Adaptive Protocol for Asymptotic Consensus for a Networked Euler-Lagrange Systems with Uncertainty

This paper investigates distributed asymptotic consensus protocol for a group of cloud connected Euler-Lagrange nonlinear systems with the presence of bounded uncertainty. The consensus protocol is designed by combining linear sliding surface vectors with robust adaptive learning algorithms. The sliding surface is designed by comprising position and velocity signals of the leader and neighboring follower Lagrange systems. Adaptive learning algorithm uses to learn and compensate bounded uncertainty associated with parameters and other external disturbance uncertainty. Lyapunov and sliding mode control theory uses to design and illustrate the convergence of the closed loop system under proposed protocol. The convergence analysis has three parts. In first part, it proves that the position and velocity consensus error states are bounded provided that the parameter estimates are continuous and hounded by positive constant. The second part guarantees that the sliding mode motion occurs for each Lagrange system in finite-time. The third part ensures that the states for a group of follower Lagrange systems can achieve asymptotic consensus tracking provided that the interaction communication topology has a directed spanning tree. This analysis shows asymptotic consensus property of the position and velocity consensus error states on the sliding mode surface. The design and implementation of the proposed asymptotic consensus protocol is easier as it does not use the exact bound of the uncertainty.