Designing Control Inputs and Inner Couplings for Controllability and Observability of Complex Dynamical Networks

Network controllability and observability are essential and key to guarantee before onecan consider how to control or predict a complex dynamical network in any application.This proposal aims to design control inputs by means of characterizing the control inputand inner coupling matrices for achieving complete state and/or structural controllabilityand/or observability of complex dynamical networks. Basic properties of control inputmatrices and their relationships with the invariant system state-controllability subspacewill be precisely characterized. Then, based on that, the inner coupling and control inputmatrices such that the overall network is completely state and/or structural controllableand/or observable. Finally, for typical fully-connected networks, trees, or cycles,establish some simple and easily-verifiable criteria for designing the inner coupling andcontrol input matrices towards their complete state and/or structural controllabilityand/or observability.?