Model Predictive Control with a Periodic Observer ($\Pi$-MPC)

This repository contains example code for Perfecting Periodic Trajectory Tracking: Model Predictive Control with a Periodic Observer by Luis Pabon, Johannes Köhler, John Irvin Alora, Patrick Benito Eberhard, Andrea Carron, Melanie N. Zeilinger, and Marco Pavone.

The repository is designed to facilitate understanding and implementation of $\Pi$-MPC using a straightforward example. We showcase the application of $\Pi$-MPC by tracking a periodic trajectory around a pendulum's unstable equilibrium. The nominal model is a linearized model that additionally has incorrect parameters (i.e. mass, length).

Getting Started

Ensure Python 3 is installed on your system. The project dependencies are listed in requirements.txt.

Installation

1. Clone the repository to your local machine.
2. Create a virtual environment (recommended) for the project to manage dependencies.
3. Install dependencies by navigating to the repository's root directory and executing:

pip install -r requirements.txt

This command installs all the necessary Python packages as specified in requirements.txt.

Running the Example

Open the provided Jupyter notebook and run the cells sequentially. The notebook will guide you through:

• Offline Design: Preparation steps and design considerations for $\Pi$-MPC.
• Online Operation and Simulation: Simulation with the pendulum tracking a periodic trajectory, demonstrating the ability of $\Pi$-MPC to achieve minimal tracking errors despite model mismatch.

Support

For questions or support, please file an issue on the GitHub repository page. Contributions and feedback are welcome.