Synchronizing Networked Lagrangian Systems via Binary Control Protocols

The binary control protocols are proposed for synchronization of networked Lagrangian systems with/without tracking. These protocols are inspired by the observed behavior in animal groups, where relative motion is determined not by full time-signal measurements, but by coarse estimates of relative heading differences between neighbors. The signum protocol does not require explicit measurement of time signals from neighbors, and hence it has the potential to significantly reduce the requirements for both computation and sensing. In the case that there exists a time-varying control node in the networked Lagrangian systems, the finite-time tracking control is achieved by using the signum protocol. Numerical examples are given to illustrate the theoretical results.