On the robustness of large 1-D network of double integrator agents

We study the robustness to external disturbances of large 1-D network of double-integrator agents with distributed control. We provide precise quantitative comparison of certain H_∞ norm between two common control architectures: predecessor-following and symmetric bidirectional. In particular, we show that the scaling laws of the H_∞ norm for predecessor-following architecture is O(α^N) (α >; 1), but only O(N³) for symmetric bidirectional architecture, where N is the number of agents in the network. The results for symmetric bidirectional architecture are obtained by using a PDE model to approximate the closed-loop dynamics of the network for large N. Numerical calculations show that the PDE approximation provides accurate predictions even when N is small. In addition, we examine the robustness of asymmetric bidirectional architecture. Numerical simulations show that with judicious asymmetry in the velocity feedback, the robustness of the network can be improved considerably over symmetric bidirectional and predecessor-following architectures.