Optimal regulator dredges underlying modularity in Input-outputs

Designing optimal regulator is one of the important branch of control theorem concerned with objective-oriented optimization. In present study we focus on the modular structure of control networks in linear state space system based on robustness to perturbations, and develop the optimal regulator which enable to dredge underlying modularity in Input-outputs. It is analyzed how networked systems shape the modular structure using stochastic linear model, which is forced to fit desired inputs-outputs, and exposed to perturbations entered from inside and outside of the system. We show that modularity can emerge while optimizing outputs, as well as enhancing robustness, that is, reducing sensitivity to perturbations. We found that the constraint to networking is generated based on robustness trade-off; suppressing one perturbation brings in amplifying another perturbation.