Shaping robust dynamic inversion control of neural cell dynamics

<i>Objective.</i>In this work, we aim to enforce the spiking of the membrane potential of a single neuron or a neuronal network, described by dynamical models, by controlling the current injection in the presence of model uncertainty and synaptic noise.<i>Approach.</i>In this study, we propose Shaping Robust Dynamic Inversion (SRDI) as a robust nonlinear control technique, which uses dynamic inversion of neuronal dynamical systems and shapes the error surface to derive a current control signal that enforces the spiking of membrane potential under model uncertainty.<i>Main results.</i>We apply SRDI to Hodgkin-Huxley model, integrate-and-fire model, and FitzHugh-Nagumo model to achieve controlled neuron spiking. Comparative studies show that SRDI outperforms classical dynamic inversion in robustness and linear model predictive control in computational time.<i>Significance.</i>SRDI enables precise and efficient neural control by shaping error dynamics, handling nonlinearities, and maintaining robustness to noise and model uncertainty, achieving controlled timing for single spikes, spike trains, and small neuronal networks.