  Because neuronal networks are intricate systems composed of interconnected
neurons, their control poses challenges owing to their nonlinearity and
complexity. In this paper, we propose a method to design control input to a
neuronal network to manipulate the firing patterns of modules within the
network. We propose a methodology for designing a control input based on
temporal deep unfolding-based model predictive control (TDU-MPC), a control
methodology based on the deep unfolding technique actively investigated in the
context of wireless signal processing. During the method development, we
address the unique characteristics of neuron dynamics, such as zero gradients
in firing times, by approximating input currents using a sigmoid function. The
effectiveness of the proposed method is confirmed via numerical simulations. In
networks with 15 and 30 neurons, the control was achieved to switch the firing
frequencies of two modules without directly applying control inputs. This study
includes a tailored methodology for networked neurons, the extension of TDU-MPC
to nonlinear systems with reset dynamics, and the achievement of desired firing
patterns in neuronal networks.
