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Ensuring Both Positivity and Stability Using Sector-Bounded Nonlinearity for Systems with Neural Network Controllers

Authors :
Hedesh, Hamidreza Montazeri
Siami, Milad
Publication Year :
2024

Abstract

This paper introduces a novel method for the stability analysis of positive feedback systems with a class of fully connected feedforward neural networks (FFNN) controllers. By establishing sector bounds for fully connected FFNNs without biases, we present a stability theorem that demonstrates the global exponential stability of linear systems under fully connected FFNN control. Utilizing principles from positive Lur'e systems and the positive Aizerman conjecture, our approach effectively addresses the challenge of ensuring stability in highly nonlinear systems. The crux of our method lies in maintaining sector bounds that preserve the positivity and Hurwitz property of the overall Lur'e system. We showcase the practical applicability of our methodology through its implementation in a linear system managed by a FFNN trained on output feedback controller data, highlighting its potential for enhancing stability in dynamic systems.<br />Comment: 6 pages, 7 figures, to be published in IEEE Control Systems Letters (L-CSS)

Details

Database :
arXiv
Publication Type :
Report
Accession number :
edsarx.2406.12744
Document Type :
Working Paper