In many problems, agents cooperate locally so that a leader or fusion center can infer the state of every agent from probing the state of only a small number of agents. Versions of this problem arise when a fusion center reconstructs an extended physical field by accessing the state of just a few of the sensors measuring the field, or a leader monitors the formation of a team of robots. Given a link cost, the paper presents a polynomial time algorithm to design a minimum cost coordinated network dynamics followed by the agents, under an observability constraint. The problem is placed in the context of structural observability and solved even when up to k agents in the coordinated network dynamics fail.
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