NARMA-L2 Neural Network Controller for Anti-Lock Braking System

A neural network-based feedback linearization controller (NARMA-L2) for optimal slip ratio regulation in an Anti-Lock Braking System (ABS), implemented from scratch based on a published research paper.

Motivation

Traditional ABS controllers rely on threshold-based logic or PID tuning, which struggle with the highly nonlinear tire-road friction dynamics. This project implements a NARMA-L2 (Nonlinear Autoregressive Moving Average - Level 2) controller that learns the nonlinear dynamics and cancels them through feedback linearization, achieving tighter slip ratio regulation than a conventional PID.

Key Results

Slip Ratio Regulation: NARMA-L2 vs PID

The NARMA-L2 controller maintains the slip ratio closer to the optimal value (0.25) compared to the PID controller, with less oscillation and faster convergence.

Tire-Road Friction Model

The system uses a quarter-car model with a nonlinear friction characteristic that peaks at the optimal slip ratio.

Neural Network Training

Both f-network and g-network converge reliably during training.

Architecture

The project implements a complete ABS simulation and control pipeline:

Quarter-Car Model          NARMA-L2 Controller          Comparison
┌──────────────────┐      ┌──────────────────────┐      ┌────────────┐
│ Vehicle dynamics │      │ f-network (nonlinear │      │ NARMA-L2   │
│ Wheel dynamics   │────▶│   dynamics)          │─────▶│ vs         │
│ Brake actuator   │      │ g-network (system    │      │ PID        │
│ Friction model   │      │   sensitivity)       │      │ controller │
└──────────────────┘      └──────────────────────┘      └────────────┘

Mathematical Model

The NARMA-L2 model decomposes the system as:

$$y(k+d) = f(\cdot) + g(\cdot) \times u(k+1)$$

Where f captures the autonomous nonlinear dynamics and g captures the system's sensitivity to the control input. Both are approximated by single-hidden-layer neural networks (5 neurons, tanh activation).

The control law inverts this model:

$$u(k+1) = \frac{y_{ref} - f(\cdot)}{g(\cdot)}$$

Project Structure

abs_narmal2/
├── ABS.ipynb                  # Main notebook with full pipeline and visualizations
├── src/
│   ├── __init__.py
│   ├── abs_simulator.py       # Quarter-car ABS model and data generation
│   ├── pid_controller.py      # PID controller with filtered derivative
│   └── narmal2_controller.py  # NARMA-L2 neural network controller
├── figures/                   # Generated plots and visualizations
├── requirements.txt
├── LICENSE
└── README.md

Getting Started

Prerequisites

• Python 3.10 or higher
• pip

Installation

git clone https://github.com/AstyanM/abs-narmal-2.git
cd abs-narmal-2
pip install -r requirements.txt

Usage

Run the full notebook:

jupyter notebook ABS.ipynb

Use the modules directly:

from src import ABSSystemSimulator, PIDController, NARMAL2Controller

# Simulate braking scenarios
simulator = ABSSystemSimulator()
data = simulator.generate_training_data(n_scenarios=50)

# Train the NARMA-L2 controller
controller = NARMAL2Controller(hidden_neurons=5)
controller.train(data, epochs=100)

# Compute control input for a given state
import numpy as np
state = np.array([0.3, 0.28, 0.25, 500, 480, 450])
u = controller.compute_control_input(state, reference_slip=0.25)

Technical Details

Component	Specification
Vehicle model	Quarter-car, 440 kg
Friction model	Nonlinear $\mu$-$\lambda$ curve (dry asphalt)
Neural networks	1 hidden layer, 5 neurons, tanh activation
Training data	50 scenarios, PID-controlled braking
Optimizer	Adam (lr=0.001)
Target slip ratio	$\lambda_0 = 0.25$

Reference

This implementation is based on:

J. O. Pedro, O. T. C. Nyandoro, S. John, "Neural Network Based Feedback Linearisation Slip Control of an Anti-Lock Braking System", 7th Asian Control Conference, Hong Kong, China, August 27-29, 2009. IEEE Xplore

Author

Martin Astyan — Architecture of Intelligent Transport Systems, 2025

License

This project is licensed under the MIT License — see LICENSE for details.