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Improving Initial Transients of Online Learning Echo State Network Control System with Feedback Adjustments

Junyi Shen

TL;DR

It is shown that the feedback controller accelerates convergence by guiding the online learning ESN to operate within a data range well-suited for learning, and shows strong robustness against changes in the controlled system's dynamics and variations in the online learning model's hyperparameters.

Abstract

Echo state networks (ESNs) have become increasingly popular in online learning control systems due to their ease of training. However, online learning ESN controllers often suffer from slow convergence during the initial transient phase. Existing solutions, such as prior training, control mode switching, and incorporating plant dynamic approximations, have notable drawbacks, including undermining the system's online learning property or relying on prior knowledge of the controlled system. This work proposes a simple yet effective approach to address the slow initial convergence of online learning ESN control systems by integrating a feedback proportional-derivative (P-D) controller. Simulation results demonstrate that the proposed control system achieves rapid convergence during the initial transient phase and shows strong robustness against changes in the controlled system's dynamics and variations in the online learning model's hyperparameters. We show that the feedback controller accelerates convergence by guiding the online learning ESN to operate within a data range well-suited for learning. This study offers practical benefits for engineers aiming to implement online learning ESN control systems with fast convergence and easy deployment.

Improving Initial Transients of Online Learning Echo State Network Control System with Feedback Adjustments

TL;DR

It is shown that the feedback controller accelerates convergence by guiding the online learning ESN to operate within a data range well-suited for learning, and shows strong robustness against changes in the controlled system's dynamics and variations in the online learning model's hyperparameters.

Abstract

Echo state networks (ESNs) have become increasingly popular in online learning control systems due to their ease of training. However, online learning ESN controllers often suffer from slow convergence during the initial transient phase. Existing solutions, such as prior training, control mode switching, and incorporating plant dynamic approximations, have notable drawbacks, including undermining the system's online learning property or relying on prior knowledge of the controlled system. This work proposes a simple yet effective approach to address the slow initial convergence of online learning ESN control systems by integrating a feedback proportional-derivative (P-D) controller. Simulation results demonstrate that the proposed control system achieves rapid convergence during the initial transient phase and shows strong robustness against changes in the controlled system's dynamics and variations in the online learning model's hyperparameters. We show that the feedback controller accelerates convergence by guiding the online learning ESN to operate within a data range well-suited for learning. This study offers practical benefits for engineers aiming to implement online learning ESN control systems with fast convergence and easy deployment.
Paper Structure (9 sections, 15 equations, 11 figures)

This paper contains 9 sections, 15 equations, 11 figures.

Figures (11)

  • Figure 1: Online learning ESN control system with feedback P-D controller.
  • Figure 2: Step responses: (a) ESN+FB; (b) ESN; (c) TESN; (d) FB.
  • Figure 3: Tracking results: (a) ESN+FB; (b) ESN; (c) TESN; (d) FB.
  • Figure 4: Feedforward and feedback control elements of the ESN+FB method: (a) Tracking the step response signal; (b) Tracking the complex signal.
  • Figure 5: Tracking a complex signal with system changes: (a) ESN+FB; (b) TESN; (c) Control errors; (d) Controller outputs. Green zones before the 2,000th step denotes the system was unchanged as (\ref{['eq: Nonlinear 1']}), grey zones after the 2,000th step means the system's dynamics has changed to (\ref{['eq: Nonlinear 2']}).
  • ...and 6 more figures