Robustness analysis for a neural network based adaptive control scheme

A recently developed approach to the control of uncertain nonlinear systems uses a neural network to improve upon dynamic inversion. In the proposed architecture, the neural network adaptively cancels inversion errors through online learning. Asymptotic stability of the closed-loop system is guaranteed based on Lyapunov analysis. In this sense, the control scheme is similar to more traditional adaptive control techniques. This approach does not account for unmodeled dynamics, however, since it assumes precise knowledge of the plant order. In this paper, singular perturbation arguments are employed to show robustness to unmodeled dynamics at the plant input. The theoretical result is illustrated using a simplified nonlinear model of the longitudinal dynamics of an air-to-air missile.