Cooperative adaptive control for synchronization of second‐order systems with unknown nonlinearities

TLDR

The study concerns multi‑agent systems with second‑order integrator dynamics, where agents may have different dynamics, the leader node is nonlinear and unknown, and the communication graph is directed with fixed topology. The authors aim to achieve synchronization to a desired trajectory for such systems despite unknown nonlinearities and disturbances. They design cooperative tracking adaptive controllers that employ neural‑network parametric approximators at each node, tuned to ensure stability and performance, and validate the design with a simulation of second‑order Lagrangian dynamics. A Lyapunov‑based analysis proves ultimate boundedness of the tracking error, and the simulation confirms the controller’s effectiveness. © 2010 John Wiley & Sons, Ltd.

Abstract

Abstract This paper studies synchronization to a desired trajectory for multi‐agent systems with second‐order integrator dynamics and unknown nonlinearities and disturbances. The agents can have different dynamics and the treatment is for directed graphs with fixed communication topologies. The command generator or leader node dynamics is also nonlinear and unknown. Cooperative tracking adaptive controllers are designed based on each node maintaining a neural network parametric approximator and suitably tuning it to guarantee stability and performance. A Lyapunov‐based proof shows the ultimate boundedness of the tracking error. A simulation example with nodes having second‐order Lagrangian dynamics verifies the performance of the cooperative tracking adaptive controller. Copyright © 2010 John Wiley & Sons, Ltd.