Control energy of complex networks towards distinct mixture states

Controlling complex networked systems is a real-world puzzle that remains largely unsolved. Despite recent progress in understanding the structural characteristics of network control energy, target state and system dynamics have not been explored. We examine how varying the final state mixture affects the control energy of canonical and conformity-incorporated dynamical systems. We find that the control energy required to drive a network to an identical final state is lower than that required to arrive a non-identical final state. We also demonstrate that it is easier to achieve full control in a conformity-based dynamical network. Finally we determine the optimal control strategy in terms of the network hierarchical structure. Our work offers a realistic understanding of the control energy within the final state mixture and sheds light on controlling complex systems.