Practical tracking synchronization of networked Lagrangian systems via pinning control

This paper is concerned with practical tracking synchronization problem for disturbed networked Lagrangian systems based on pinning control framework. We propose a pinning algorithm to guarantee the practical tracking synchronization of networked identical Lagrangian systems by applying local linear feedback injections to a small fraction of nodes. We also present a simple yet generic criteria on pinning synchronization for such algorithm over undirected connected graphs, where all the agents are regulated to follow a desired time-varying target trajectory with a desired tracking error bound. It is worth noting that pinning control and local linear feedback control techniques have not yet been used to study the synchronization and control of networked Lagrangian systems, due to the strong nonlinearity of the Lagrangian system. Pinning control is used to study synchronization of networked Lagrangian systems in our paper, which further extends the ideals and techniques presented in previous works on Lagrangian systems. As a direct application of the theoretical results, synchronization of eight two-link revolute manipulators is simulated and discussed in detail. Numerical experiments verify the effectiveness of the proposed control technique.