Stability analysis of reservoir computers dynamics via Lyapunov functions

Abstract

A Lyapunov design method is used to analyze the nonlinear stability of a generic reservoir computer for both the cases of continuous-time and discrete-time dynamics. Using this method, for a given nonlinear reservoir computer, a radial region of stability around a fixed point is analytically determined. We see that the training error of the reservoir computer is lower in the region where the analysis predicts global stability but is also affected by the particular choice of the individual dynamics for the reservoir systems. For the case that the dynamics is polynomial, it appears to be important for the polynomial to have nonzero coefficients corresponding to at least one odd power (e.g., linear term) and one even power (e.g., quadratic term).

Document Details

Document Type
Pub Defense Publication
Publication Date
Oct 01, 2019
Source ID
10.1063/1.5123733

Entities

People

  • Afroza Shirin
  • Francesco Sorrentino
  • Isaac Klickstein

Organizations

  • Defense Threat Reduction Agency
  • National Science Foundation
  • Office of Naval Research
  • University of New Mexico

Tags

Fields of Study

  • Mathematics

Readers

  • Control Systems Engineering.
  • Hydrologic Risk Analysis and Mitigation.