Chaotic Systems and Control of Chaos — Lesson 3

This lesson covers the final class of a course on non-linear vibration, summarizing all the topics studied throughout the course. It delves into the chaotic system and control of chaos, discussing different types of responses, such as fixed point response, periodic response, quasi-periodic response, and chaotic responses. The lesson also explores the study of chaos, an emerging field with numerous practical applications, including stabilization, synchronization, and bifurcation control. It further discusses the use of adaptive control, sliding mode control, and backstepping control for synchronization. The lesson concludes with a review of various research papers on the subject, highlighting the wide range of applications of non-linear vibration and chaos control.

Video Highlights

01:00 - Introduction
08:00 - Script for solution
16:00 - References for chaos in dynamic analysis systems
45:00 - Applications of chaotic systems
53:00 - Two degree of freedom systems 

Key Takeaways

- Non-linear vibration and chaos control have numerous practical applications, including in stabilization, synchronization, and bifurcation control.
- The study of chaos is an emerging field with a lot of literature available for further exploration.
- Different types of responses, such as fixed point response, periodic response, quasi-periodic response, and chaotic responses, can be characterized using time response, phase portrait, Poincare section, FFT, and Lyapunov exponents.
- Adaptive control, sliding mode control, and backstepping control are used for synchronization in chaotic systems.
- A wide range of research papers are available on the subject, highlighting the extensive applications of non-linear vibration and chaos control.