Chaos Theory & Non-Linear Sys Analysis/Control?

In summary, the conversation delves into the topic of aerospace vehicles and their software systems, specifically the progression from linear and predictable systems to non-linear and probabilistic systems. The concept of aerodynamic angle of attack is used as an example, with the early days of aircraft focusing on a linear range and later realizing the benefits of maneuvering at higher angles. The conversation also touches on the use of Chaos Theory in designing optimal systems and the request for references or citations on this topic.
  • #1
RainmanAero
83
0
Hello learned colleagues and other deep thinkers:

This question may be construed as either way too esoteric, or simply as too vague for this forum, and if deemed either of these I would agree if others find it an inappropriate topic. However...

When it comes to aerospace vehicles and the software systems that control them, I do believe the history of development has shown a marked progression from "linear and highly-predictable" systems towards an acceptance of "non-linear and more probablistic" systems. The best example I can give is aerodynamic angle of attack.

The early days of aircraft respected, honored, dare we say "worshipped" the linear angle of attack range for lift production... Generally from 0 to 18-20 degrees AOA MAX, depending upon the specific airframe/powerplant design and when its control response becomes non-linear.

We then have progressed to understanding the benefits and trade-offs of being able to maneuver aircraft at MUCH higher AoA's which are WELL into the non-linear region of aerodynamic response.

And then there is the science of Chaos Theory which bridges the worlds of linear and non-linear phenomenon with such tools as fractal embedding analytical processes (wavelets is just one of them!).

But does anyone have any references and/or citations of people who have actually used Chaos Theory as a means to design an optimal system which responds with minimum energy in both its linear and non-linear operating regions?

Thank you. I appreciate any answers or even willingness to discuss such a topic.

Rainman
 
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  • #2
I am sorry rainman I cannot be of too much help here. Moreover, I want to know what do you mean with non linear aerodynamic response?. Even though my whole research goes about fluid mechanics, I am not familiar with its engineering applications to wing aerodynamics. Maybe I am too young for knowing about everything...:biggrin:
 
  • #3


Thank you for bringing up this interesting topic, Rainman. Chaos theory and non-linear systems analysis/control are indeed relevant and important concepts in the field of aerospace engineering and control systems design.

To answer your question about the use of chaos theory in designing optimal systems, there have been some studies and applications in this area. One example is the use of chaos theory in designing optimal control strategies for chaotic systems, such as chaotic pendulums or double pendulums. These systems have highly non-linear behavior and can be difficult to control using traditional methods. By using chaos theory, researchers have been able to develop control strategies that take advantage of the inherent chaotic dynamics of these systems to achieve optimal performance.

Another application of chaos theory in control systems design is in the field of chaotic synchronization. This involves synchronizing two or more chaotic systems, such as chaotic circuits, using control signals. This has potential applications in secure communication systems and has been studied extensively in recent years.

In terms of references, there are several books and research papers available on the topic of chaos theory and control systems. One book that I would recommend is "Chaos and Nonlinear Dynamics: An Introduction for Scientists and Engineers" by Robert C. Hilborn. This book provides a comprehensive introduction to chaos theory and its applications in various fields, including control systems.

I hope this helps to answer your question and sparks further discussion on this fascinating topic. Thank you for bringing it up for consideration.
 

1. What is chaos theory?

Chaos theory is a branch of mathematics and science that studies the behavior of complex and dynamic systems that are highly sensitive to initial conditions. It explains how seemingly random and unpredictable patterns can emerge from simple and deterministic systems.

2. How is chaos theory applied in real life?

Chaos theory has applications in various fields such as physics, biology, economics, and engineering. It can be used to model weather patterns, predict stock market fluctuations, understand population dynamics, and improve control systems in engineering.

3. What is the difference between linear and non-linear systems?

Linear systems follow the principle of superposition, meaning that the output is directly proportional to the input. Non-linear systems, on the other hand, do not follow this principle and can exhibit complex and unpredictable behavior. Chaos theory deals with non-linear systems.

4. How does chaos theory relate to control theory?

Chaos theory and control theory are closely related, as chaos can occur in systems that are being controlled. Control theory aims to regulate and stabilize systems, while chaos theory explains the limits of predictability and control in complex systems.

5. Can chaos theory be used to make accurate predictions?

Chaos theory does not provide precise predictions, as it deals with systems that are highly sensitive to initial conditions. However, it can provide insights into the general behavior and patterns of complex systems, which can be useful in making informed decisions.

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