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Updated: Jun 11, 2026

WheelCon: A Wheel Control-Based Gaming Platform for Studying Human Sensorimotor Control

WheelCon: A Wheel Control-Based Gaming Platform for Studying Human Sensorimotor Control

Published on: August 15, 2020

Robust adaptive backstepping control of uncertain Lorenz system.

Hossein Nejat Pishkenari¹, Nader Jalili, Seyed Hanif Mahboobi

¹Center of Excellence in Design, Robotics and Automation (CEDRA), School of Mechanical Engineering, Sharif University of Technology, Tehran 11365-9567, Iran.

Chaos (Woodbury, N.Y.)

|July 2, 2010

Summary

This study introduces a robust adaptive control method for the Lorenz chaotic system. The novel backstepping controller is singularity-free, globally stable, and requires only one system state measurement, effectively handling parameter uncertainty.

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Published on: August 15, 2020

Area of Science:

Chaos theory
Nonlinear dynamics
Control systems engineering

Background:

The Lorenz chaotic attractor is a fundamental model in chaos theory, exhibiting sensitive dependence on initial conditions.
Traditional backstepping control methods for chaotic systems can suffer from singularity issues.
Practical applications often face challenges with complete state measurement and parameter uncertainties.

Purpose of the Study:

To propose a novel robust adaptive control method for the Lorenz chaotic attractor.
To develop a singularity-free backstepping controller based on the Lyapunov stability theorem.
To address the practical limitations of state measurement unavailability and parameter uncertainty.

Main Methods:

A new backstepping control strategy is designed for the Lorenz system, leveraging its inherent properties to avoid singularities.
Lyapunov stability theorem is employed to guarantee global stability of the closed-loop system.
An adaptive identification scheme is integrated with a modified Lyapunov function to manage parameter uncertainties and ensure a negative definite derivative.

Main Results:

The proposed controller is demonstrated to be singularity-free, overcoming a key limitation of conventional methods.
Global stability of the controlled Lorenz system is proven using Lyapunov stability analysis.
The controller's effectiveness is validated through simulations, showing successful control with only one state measurement and robustness to parameter variations.

Conclusions:

The novel robust adaptive control method effectively controls the Lorenz chaotic attractor.
The singularity-free backstepping controller offers a significant advancement for chaotic system control.
The approach is practical for real-world applications due to its reduced state dependency and robustness to uncertainties.