  Objective. Precise control of neural systems is essential to experimental
investigations of how the brain controls behavior and holds the potential for
therapeutic manipulations to correct aberrant network states. Model predictive
control, which employs a dynamical model of the system to find optimal control
inputs, has promise for dealing with the nonlinear dynamics, high levels of
exogenous noise, and limited information about unmeasured states and parameters
that are common in a wide range of neural systems. However, the challenge still
remains of selecting the right model, constraining its parameters, and
synchronizing to the neural system. Approach. As a proof of principle, we used
recent advances in data-driven forecasting to construct a nonlinear
machine-learning model of a Hodgkin-Huxley type neuron when only the membrane
voltage is observable and there are an unknown number of intrinsic currents.
Main Results. We show that this approach is able to learn the dynamics of
different neuron types and can be used with MPC to force the neuron to engage
in arbitrary, researcher-defined spiking behaviors. Significance. To the best
of our knowledge, this is the first application of nonlinear MPC of a
conductance-based model where there is only realistically limited information
about unobservable states and parameters.
