Constructive RNNs: An Error-Recurrence Perspective on Time-Variant Zero Finding Problem Solving Under Uncertainty

TL;DR

This paper introduces a control-theoretic approach to designing error-recurrence neural networks with finite-time convergence and robustness for time-variant problems, improving accuracy and stability under uncertainties.

Contribution

It proposes novel rectifying actions and uncertainty compensation techniques to achieve fixed-time convergence and robustness in RNNs for time-variant zero-finding problems.

Findings

Achieves fixed-time convergence of RNN models.

Enhances robustness against uncertainties in time-variant problems.

Provides theoretical guarantees for convergence and stability.

Abstract

When facing time-variant problems in analog computing, the desirable RNN design requires finite-time convergence and robustness with respect to various types of uncertainties, due to the time-variant nature and difficulties in implementation. It is very worthwhile to explore terminal zeroing neural networks, through examining and applying available attracting laws. In this paper, from a control-theoretic point of view, an error recurrence system approach is presented by equipping with uncertainty compensation in the pre-specified error dynamics, capable of enhancing robustness properly. Novel rectifying actions are designed to make finite-time settling so that the convergence speed and the computing accuracy of time-variant computing can be improved. Double-power and power-exponential rectifying actions are respectively formed to construct specific models, while the particular expressions of settling time function for the former are presented, and for the latter the proximate settling-time estimations are given, with which the fixed-time convergence of the corresponding models is in turn established. Moreover, the uncertainty compensation by the signum/smoothing-signum techniques are adopted for finite-duration stabilization. Theoretical results are presented to demonstrate effectiveness (involving fixed-time convergence and robustness) of the proposed computing schemes for the time-variant QP problem solving.