Optimal rendezvous control for randomized communication topologies

In this paper we analyze randomized coordination control strategies for the rendezvous problem of multiple agents subject to input and measurement disturbances. The performance of these control strategies is measured in terms of three important metrics: average relative agents´ distance, average input energy consumption, and number of packets per unit time that each agent can receive from the other agents. By adopting an LQ-like optimal control approach, we show how to numerically compute optimal feedback gains for randomized communication topologies. In particular we show that there is a trade off between these three metrics and that the optimal feedback is a sum of two terms: one that depends only the agents own positions and the other that depends only on relative distances between agents. We also show that randomly switching communication links allows for greater performance as compared to fixed communication topologies