Distributed adaptive controller design for the unknown networked Lagrangian systems

A Lyapunov technique is presented to design a synchronization protocol for a group of Lagrangian systems with a target system to be tracked. All the systems can have different dynamics. Compared with the previous work in the context of Lagrangian systems control, the development is for more general directed communication graph topology, which is only required to have a spanning tree. The dynamics of the networked systems as well as the target system are all assumed unknown. A neural network is used at each node to approximate the distributed dynamics. The resulting protocol consists of a simple decentralized proportional-plus-derivative (PD) term and a nonlinear term with distributed adaptive tuning laws at each node.