Protection ellipsoids for stability analysis of feedforward neural-net controllers

In this paper, we consider a feedforward neural network for the control of a class of multi-input, multi-output nonlinear systems. While feedforward neural networks offer a simple and appealing approach to enhance the trajectory tracking performance of the closed loop system, stability analysis is often more difficult than the conventional implementation of a neural network embedded within the feedback path. We present a stability theorem which guarantees that the closed loop system is uniformly bounded. We derive conditions on the feedback gain matrices that guarantee this bound. Additionally, we outline a generalization to the non-symmetric case.