Analysis and Design of Quadratic Neural Networks for Regression, Classification, and Lyapunov Control of Dynamical Systems

TL;DR

This paper explores quadratic neural networks for regression, classification, and control of dynamical systems, highlighting their convex training, analytical expressiveness, and efficiency with limited data.

Contribution

It introduces a novel quadratic neural network architecture with convex training and analytical input-output mapping, applicable to various system tasks.

Findings

Networks achieve global optimality in training.

Effective with small training datasets.

Successful applications in system identification and control.

Abstract

This paper addresses the analysis and design of quadratic neural networks, which have been recently introduced in the literature, and their applications to regression, classification, system identification and control of dynamical systems. These networks offer several advantages, the most important of which are the fact that the architecture is a by-product of the design and is not determined a-priori, their training can be done by solving a convex optimization problem so that the global optimum of the weights is achieved, and the input-output mapping can be expressed analytically by a quadratic form. It also appears from several examples that these networks work extremely well using only a small fraction of the training data. The results in the paper cast regression, classification, system identification, stability and control design as convex optimization problems, which can be solved efficiently with polynomial-time algorithms to a global optimum. Several examples will show the effectiveness of quadratic neural networks in applications.