Optimal control/observation points problem and separation principle of weakly controlled large-scaled multi-agent systems

In this paper, we deal with the problem of finding optimal control/observation points of large-scaled multi-agent systems. We consider a kind of reference following of the systems with a support of external optimal output feedback control called “weak control” under a limitation of the number of control/observation points and show that the optimal control/observation points for it can be obtained by the left/right zero eigenvectors of the network matrix. By employing this result, the computation complexity for finding the optimal control/observation points in the large-scaled multi-agent systems is drastically reduced compared to a brute-force searching method. We also remark that “a separation principle” holds in this optimal control/observation points problem.