Course11710648363 lectures
Nonlinear Dynamical Systems and Control
Prof. Vijaysekhar Chellaboina · IIT Madras
About
The course will provide an introduction to stability and control of nonlinear systems described by ordinary differential equations. The first part of the course will focus on the asymptotic analysis of nonlinear systems through Lyapunov function methods. The second part of the course will provide applications of the Lyapunov function approach to control of linear and nonlinear systems. The specific topics include robust control, adaptive control, and feedback linearization.
Intended audience: PG/PhD students
Prerequisites: B. Tech/B.E with a background in Control Systems or Linear Control Systems
Lectures
Week 1
- Introduction - Part 1
- Introduction - Part 2
- Ordinary Differential Equations - Part 1
- Ordinary Differential Equations - Part 2
- ODE Solutions via Examples
Week 2
- Solutions to ODEs
- Existence and Uniqueness Theorems
- Asymptotic Behaviour of Dynamical Systems: Part 1
- Asymptotic Behaviour of Dynamical Systems: Part 2
- Asymptotic Behaviour of Dynamical Systems: Part 3
Week 3
- Stability Theory: Definitions - Part 1
- Stability Theory: Definitions - Part 2
- Stability Theory: Lyapunov Methods - Part 1
- Stability Theory: Lyapunov Methods - Part 2
- Lyapunov Function Examples
Week 4
- LaSalle's Invariance Theorem
- Stability Theory: Converse Lyapunov & Instability Theorems
- Solved Problems - Part 1
- Solved Problems - Part 2
Week 5
- Linear Systems - Part 1
- Linear Systems - Part 2
- Linearization of Nonlinear Systems
- Linear Systems & Linearization: Solved Problems - Part 1
- Linear Systems & Linearization: Solved Problems - Part 2
Week 6
- Nonlinear Analysis: Key Concepts and Results - Part 1
- Nonlinear Analysis: Key Concepts and Results - Part 2
- Construction of Lyapunov Functions - Part 1
- Construction of Lyapunov Functions - Part 2
- Futher Topics - Part 1
- Futher Topics - Part 2
Week 7
- Introduction to Robust Stability
- Robust Stability for Structured Uncertainty - Part 1
- Robust Stability for Structured Uncertainty - Part 2
- Robust Stability for Structured Uncertainty - Part 3
- The Absolute Stability (Lure) Problem
- Robust Stability: A Solved Problem
Week 8
- Dissipativity Theory - Part 1
- Dissipativity Theory - Part 2
- Dissipativity: Solved Problems
- Feedback Interconnection of Dissipative Systems - Part 1
- Feedback Interconnection of Dissipative Systems - Part 2
Week 9
- Stable Adaptive Control - Part 1
- Stable Adaptive Control - Part 2
- Examples & Generalizations - Part 1
- Examples & Generalizations - Part 2
- Optimization - Part 1
- Optimization - Part 2
Week 10
- Functional Optimization - Part 1
- Functional Optimization - Part 2
- Optimal Control - Part 1
- Optimal Control - Part 2
- Optimal Feedback Control
Week 11
- Stability Margins of Feedback Controllers
- Control Lyapunov Functions
- Disturbance Rejection - Part 1
- Disturbance Rejection - Part 2
- Revisition through Solved Problems I
- Revisition through Solved Problems I(Continued)
Week 12
Syllabus and materials
At NPTEL, as the course publishes them.
Credits and licence
- Institution
- IIT Madras
- Department
- Electrical Engineering
- Teacher
- Prof. Vijaysekhar Chellaboina
- Level
- Graduate
- Language
- English
- Subjects
- Engineering
- Source
- NPTEL
- Licence
- CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
- Attribution
- NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
- Who can watch
- NPTEL gives no rating. Invisible Network shows it to Tweens profiles and older, judged from what the source says about it. How courses are placed
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