In this dissertation, neural networks (NN) approximate unknown nonlinear functions in the system equations, unknown control inputs, and cost functions for two different classes of nonlinear discrete-time systems. Employing NN in closed-loop feedback systems requires that weight update algorithms be stable...Controllers are developed and applied to a nonlinear, discrete-time system of equations for a spark ignition engine model to reduce the cyclic dispersion of heat release --Abstract, page iv