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In real-world social infrastructures such as power systems, proven controllers are already implemented and operated stably. To further improve the control performance reliably, bi-layered control with inheriting the existing controller is proposed: the existing controller generates the baseline control signal in the upper layer, while multiple sub-controllers individually coordinate the signal to actuate the infrastructure system in the lower layer. The sub-controllers are characterized by few parameters that represent the degree of coordination. Then, the update strategy of the parameter with guaranteeing the safety of the overall system is proposed. The effectiveness of the bi-layered control is shown via a numerical experiment with a power system model.