Communication-aware Multi-agent Systems Control Based on $k$-hop Distributed Observers

We propose a distributed control strategy to allow the control of a multi-agent system requiring k-hop interactions based on the design of distributed state and input observers. In particular, we design for each agent a finite time convergent state and input observer that exploits only the communication with the 1-hop neighbors to reconstruct the information regarding those agents at a 2-hop distance or more. We then demonstrate that if the k-hop based control strategy is set-Input to State Stable with respect to the set describing the goal, then the observer information can be adopted to achieve the team objective with stability guarantees.