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ReservoirComputing-with-EchoStateNetworks-for-an-InvertedPendulum-closed-loop-system

Echo State Networks in Reservoir Computing for a Custom Closed-Loop Inverted Pendulum

Project Goals

  1. Explore the application of Echo State Networks (ESNs) within the Reservoir Computing (RC) framework for controlling a custom closed-loop inverted pendulum system.
  2. Demonstrate the effectiveness of ESN-based RC in modeling and controlling complex nonlinear dynamics.
  3. Provide a practical example of implementing ESN-based RC using the PyTorch and ReservoirPy Python packages.

Project Description

This project implements an ESN-based RC model for controlling a custom closed-loop inverted pendulum system. The notebook leverages PyTorch and ReservoirPy to explore how ESNs can be used to model and control nonlinear systems with high-dimensional dynamics. The project follows these steps:

  1. System Dynamics Definition: Define the dynamics of the inverted pendulum, including its equations of motion and control inputs.
  2. Reservoir Setup: Configure the ESN reservoir with appropriate hyperparameters, including the number of neurons, spectral radius, and input scaling factors.
  3. Training the ESN: Train the ESN using a dataset generated from the inverted pendulum system, where the control signal serves as the input and the pendulum’s angle and angular velocity are the outputs.
  4. Performance Evaluation: Assess the ESN’s performance by comparing its predictions to the actual system dynamics.

Implementation Files

1.cart_pendulum_model.py: Defines the dynamics of the custom inverted pendulum system.

  1. cart_pendulum_measurement.py: Defines the measurement for the custom closed-loop inverted pendulum system.

  2. controller.py: Implements the closed-loop PID controller to control the inverted pendulum system.

Notebooks

  1. ESN-observation-cartpole.ipynb: Demonstrates the ESN-based RC model for observing of the latent states of the pendulum system.

  2. ESN-prediction-cartpole.ipynb: Demonstrates the ESN-based RC model for predicting the future dynamics of the custom closed-loop inverted pendulum system.

Usage Instructions

To run this notebook, follow these steps:

  1. Install Required Packages: Ensure that the necessary Python packages are installed: 
    pip install torch reservoirpy
  2. Download the Notebook: Obtain the notebook from the provided link or repository.
  3. Run the Notebook: Open the notebook in a Jupyter environment or any Python-compatible IDE.
  4. Execute the Code: Run the cells in sequence to implement the ESN-based RC model for the custom closed-loop inverted pendulum system.
  5. Analyze Results: Review the results to evaluate the ESN model's effectiveness in controlling the system.

References

  1. PyTorch Documentation
  2. ReservoirPy Documentation

Notes

This notebook provides a foundational implementation of ESN-based RC for a custom closed-loop inverted pendulum system. Depending on your specific needs and problem domain, you may need to modify and extend the code.