A control-theoretic study of complex systems such as closed-loop neural prostheses exhibits several challenges, from the design of an optimal feedback control problem to its solution. In this paper we study one such system, a closed-loop voluntary movement of a prosthetic finger using electrophysio- logical activities of a single cortical motor neuron. We develop an optimal feedback control problem in the nonlinear receding horizon based terminal set constraint framework. We analyze the feasibility and stability of the control problem. Further, we solve the control problem numerically by implementing a local optimum based nonconvex nonlinear programming algorithm. Finally, we study effects of visual and proprioceptive feedback pathways on the closed-loop system. Our results elucidate the importance of multiple feedback paths in designing a closed-loop neural prosthetic system.