Limit cycle oscillations (LCOs) affect current fighter aircraft and are expected to be present on next generation fighter aircraft. Current efforts in control systems designed to suppress LCO behavior have either used a linear model, restricting the flight regime, require exact knowledge of the system dynamics, or require uncertainties in the system dynamics to be linear-in-the-parameters and only present in the torsional stiffness. Furthermore, the aerodynamic model used in prior research efforts neglects nonlinear effects. This paper presents the development of a controller consisting of a continuous robust integral of the sign of the error (RISE) feedback term with a neural network (NN) feedforward term to achieve asymptotic tracking of uncertainties that do not satisfy the linear-in-the-parameters assumption. Simulation results are presented to validate the performance of the developed controller.