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Control Systems

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Control systems are everywhere in contemporary society, influencing diverse applications from aerospace to automated manufacturing. These systems can be found naturally within biological processes, such as blood sugar regulation and heart rate adjustment in response to stress, as well as in man-made systems like elevators and automated vehicles. A control system is essentially a network of subsystems and processes that collaboratively convert specific inputs into desired outputs.
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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

Optimal control in a noisy system.

F Asenjo¹, B A Toledo, V Muñoz

¹Departamento de Física, Facultad de Ciencias, Universidad de Chile, Santiago, Chile.

Chaos (Woodbury, N.Y.)

|December 3, 2008

Summary

This study introduces a novel optimization method for controlling unstable periodic orbits (UPOs) amidst noise. The technique effectively stabilizes UPOs in chaotic systems, even when noise levels increase, by calculating a precise control matrix.

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Last Updated: Jun 27, 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

Area of Science:

Nonlinear Dynamics
Chaos Theory
Control Theory

Background:

Unstable periodic orbits (UPOs) are fundamental in understanding chaotic systems.
Controlling UPOs is crucial for harnessing chaotic dynamics but challenging in noisy environments.

Purpose of the Study:

To develop a robust method for controlling UPOs in the presence of noise.
To adapt control strategies for varying noise intensities and system complexities.

Main Methods:

Formulating control as an optimization problem to derive a control matrix (A).
Applying the method to the Rossler, Lorenz, and a hyperchaotic system.
Utilizing Lyapunov exponents and singular value decomposition (SVD) for analysis and noise reduction.

Main Results:

The control strategy effectively stabilizes UPOs in tested chaotic systems, even with added noise.
For low noise, a simple control matrix suffices; higher noise necessitates a full matrix.
A noise-cleaning strategy using SVD improves UPO and exponent estimation.

Conclusions:

The proposed optimization-based control is effective for stabilizing UPOs in noisy chaotic systems.
The method's adaptability to noise levels and system types makes it broadly applicable.
The SVD-based noise reduction technique offers a consistent approach for experimental applications.