Observed Control for NMPC

This project is a Python implementation of the Observed Control algorithm for Nonlinear Model Predictive Control (NMPC), as described in the paper "Observed Control: Linearly Scalable Nonlinear Model Predictive Control with Adaptive Horizons" (Hamzezadeh & Petruska, arXiv:2508.13339v1).

The core of the project is a flexible and extensible framework for defining dynamic systems and anticipated future conditions (costs), using autograd for automatic differentiation of all necessary Jacobians and Hessians.

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Features

• Efficient NMPC Solver: Implements Algorithm 3 ("Efficient Observed Control") from the reference paper, providing a computationally efficient NMPC solution with linear scalability.
• Adaptive Horizon: The controller dynamically adjusts the prediction horizon based on convergence criteria.
• Extensible Framework: Uses abstract base classes for DynamicSystem and AnticipatedCondition, allowing you to easily define custom models and cost functions.
• Automatic Differentiation: Leverages autograd to automatically compute the complex gradients and Hessians required by the algorithm, making it easy to use with new models.
• Specialized Solvers: Includes optimized analytical solvers for linear time-invariant (LTI) systems to improve speed and accuracy where applicable.
• Robust Testing: Includes a test suite using pytest to ensure the correctness of the implementation.

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Project Structure

The repository is organized into several key directories:

• core/: Contains the central logic of the Observed Control algorithm (observed_control.py) and the abstract base classes for dynamic systems (dynamic_system.py) and cost functions (anticipated_condition.py).
• systems/: Provides concrete implementations of dynamic systems, such as a general LinearSystem and a nonlinear CartPoleSystem.
• conditions/: Contains concrete implementations of cost functions, such as the common QuadraticCost.
• examples/: Includes standalone scripts that demonstrate how to use the controller for different tasks.

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Installation

To get started, clone the repository and install the necessary dependencies in a virtual environment.

# 1. Clone the repository
git clone git@github.com:M3R-CSM/observed_control.git
cd observed_control

# 2. Create and activate a virtual environment
python -m venv .venv
source .venv/bin/activate  # On Windows use: .venv\Scripts\activate

# 3. Install the project in editable mode with development tools
pip install -e .[dev]

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Running the Examples

The examples/ directory contains scripts that demonstrate the controller's functionality.

Mass-Spring-Damper System

This example demonstrates the controller driving a simple linear mass-spring-damper system to a target state of position=1.0.

To run:

python examples/msd_control_simulation.py

This will generate a plot showing the system's state (position and velocity) and the control input over time as it reaches the target.

Cart-Pole Swing-Up

This more complex example showcases the NMPC controller performing a swing-up maneuver for an underactuated cart-pole system—a classic nonlinear control problem. The goal is to swing the pole from a downward-hanging position to an upright, balanced position.

To run:

python examples/cart_pole_swing_up.py

This script will produce both an animation of the cart-pole swing-up and a plot of the state and control histories.

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Development

Running Tests

To run the entire test suite, execute the following command from the project root:

pytest

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Reference Paper

This implementation is based on the following work. Please refer to it for a detailed theoretical background on the algorithm.

Hamzezadeh, E. T., & Petruska, A. J. (2025). Observed Control: Linearly Scalable Nonlinear Model Predictive Control with Adaptive Horizons. arXiv preprint arXiv:2508.13339.