Protection ellipsoids for stability analysis of feedforward neural-net controllers

Authors:
Abraham K. Ishihara;Shahar Ben-Menahem;Nhan Nguyen
Affiliations:
Department of Electrical and Computer Engineering, Carnegie Mellon University Silicon Valley, Moffett Field, CA;Department of Physics, Stanford University, Stanford, CA and Avago Technologies, San Jose, CA;NASA Ames Research Center, Moffett Field, CA
Venue:
IJCNN'09 Proceedings of the 2009 international joint conference on Neural Networks
Year:
2009

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Abstract

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.