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PID Tuning using Cross-Entropy Deep Learning: a Lyapunov Stability Analysis

Hector Kohler, Benoit Clement, Thomas Chaffre, Gilles Le Chenadec

TL;DR

The paper tackles robust PID tuning for underwater vehicles subject to external disturbances by introducing a learning-based adaptive controller that automatically adjusts PID gains through an artificial neural network trained with the Cross-Entropy Method. Stability is analyzed within a Lyapunov framework, and the ANN-obtained gains are mapped to a parameter space that can be checked against Lyapunov criteria. Experiments in a Gazebo-based UUV simulation show that the LB PID can match the state stability of a Lyapunov-designed baseline and exhibit improved resilience to process variation, particularly under uncertain sensing and actuation. The work demonstrates the feasibility of gradient-free, data-driven PID tuning for safe and autonomous UUV operation and highlights the potential to integrate stability constraints directly into the learning process.

Abstract

Underwater Unmanned Vehicles (UUVs) have to constantly compensate for the external disturbing forces acting on their body. Adaptive Control theory is commonly used there to grant the control law some flexibility in its response to process variation. Today, learning-based (LB) adaptive methods are leading the field where model-based control structures are combined with deep model-free learning algorithms. This work proposes experiments and metrics to empirically study the stability of such a controller. We perform this stability analysis on a LB adaptive control system whose adaptive parameters are determined using a Cross-Entropy Deep Learning method.

PID Tuning using Cross-Entropy Deep Learning: a Lyapunov Stability Analysis

TL;DR

The paper tackles robust PID tuning for underwater vehicles subject to external disturbances by introducing a learning-based adaptive controller that automatically adjusts PID gains through an artificial neural network trained with the Cross-Entropy Method. Stability is analyzed within a Lyapunov framework, and the ANN-obtained gains are mapped to a parameter space that can be checked against Lyapunov criteria. Experiments in a Gazebo-based UUV simulation show that the LB PID can match the state stability of a Lyapunov-designed baseline and exhibit improved resilience to process variation, particularly under uncertain sensing and actuation. The work demonstrates the feasibility of gradient-free, data-driven PID tuning for safe and autonomous UUV operation and highlights the potential to integrate stability constraints directly into the learning process.

Abstract

Underwater Unmanned Vehicles (UUVs) have to constantly compensate for the external disturbing forces acting on their body. Adaptive Control theory is commonly used there to grant the control law some flexibility in its response to process variation. Today, learning-based (LB) adaptive methods are leading the field where model-based control structures are combined with deep model-free learning algorithms. This work proposes experiments and metrics to empirically study the stability of such a controller. We perform this stability analysis on a LB adaptive control system whose adaptive parameters are determined using a Cross-Entropy Deep Learning method.
Paper Structure (17 sections, 13 equations, 16 figures)

This paper contains 17 sections, 13 equations, 16 figures.

Table of Contents

  1. Introduction
  2. Related work
  3. AUV modeling and simulation
  4. AUV model
  5. ROS packages
  6. Our learning-based adaptive control framework
  7. PID tuning using Deep learning
  8. Learning with the Cross entropy method
  9. Experiments and Analysis
  10. Experimental settings
  11. Simulation:
  12. Training setup:
  13. Stability metrics:
  14. Evaluation setup:
  15. Control performance
  16. ...and 2 more sections

Figures (16)

  • Figure 1: Block diagram of the proposed method for PID tuning loop using Cross-Entropy Deep Learning.
  • Figure 2: Control performance without disturbance.
  • Figure 3: Control performance with noisy position and orientation measurements.
  • Figure 4: Control performance with noisy control inputs and sea current disturbance.
  • Figure 5: The position and orientation errors of the naive PID during a non-disturbed episode.
  • ...and 11 more figures