We propose to use the Izhikevich single neuron model to represent a motor cortex neuron for studying a control-theoretic perspective of a neuroprosthetic system. The problem of estimating model parameters is addressed when the only available data from intracortical recordings of a neuron are the Inter-Spike Intervals (ISIs). Non-linear constrained and unconstrained optimization problems are formulated to estimate model parameters as well as synaptic inputs using ISIs data. The primal-dual interior-point method is implemented to solve the constrained optimization problem. Reasonable model parameters are estimated by solving these optimization problems which may serve as a template for studying and developing a model of ensemble cortical neurons for neuroprosthesis applications.