On the optimal localized feedback design for multi-vehicle systems

We consider the design of localized feedback gains using relative information exchange between vehicles. The optimal controller is obtained by minimizing the global performance measure that quantifies the coherence of the large-scale network. For undirected connected graphs we show convexity of this optimal control problem, implying that its global solution can be computed efficiently. Moreover, we determine analytically the optimal localized gains for several graphs. This allows us to quantify scaling of the performance measure with the network size and to identify graphs that are favorable for maintaining coherence of the network. Another contribution of the paper lies in the characterization of all stabilizing localized feedback gains. This characterization can be utilized to examine the interplay between the underlying communication topology and the dynamics of the closed-loop system.