Nonlinear Dynamical Systems and Control

By Prof. Vijaysekhar Chellaboina | IIT Madras

Learners enrolled: 718 | Exam registration: 47

ABOUT THE COURSE:
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

INDUSTRY SUPPORT: Aerospace Industry/Chemical Process Industry

Summary

Course Status :	Ongoing
Course Type :	Elective
Duration :	12 weeks
Category :	Electrical, Electronics and Communications Engineering Mechanical Engineering Aerospace Engineering Control and Instrumentation Flight Mechanics
Credit Points :	3
Level :	Postgraduate
Start Date :	22 Jul 2024
End Date :	11 Oct 2024
Enrollment Ends :	05 Aug 2024
Exam Registration Ends :	16 Aug 2024
Exam Date :	27 Oct 2024 IST

Note: This exam date is subjected to change based on seat availability. You can check final exam date on your hall ticket.

Page Visits

Course layout

Week 1: Theory: Introduction and preliminaries - Examples and definitions of nonlinear models; state and equilibrium; existence and uniqueness through examples

Week 2: Theory: Existence and uniqueness of solutions, dependence on initial conditions

Week 3: Theory: Stability Theory I - Lagrange, Lyapunov, and asymptotic stability, Lyapunov method and theorems

Week 4: Theory: Stability Theory II - Invariant set theorems and Chetaev’s theorem for instability

Week 5: Theory: Linear Systems and Linearization

Week 6: Theory: Construction of Lyapunov functions

Week 7: Applications: Robust stability and Lure problem - Structured and sector uncertainities

Week 8: Applications: Passivity and dissipativity - General theory, Applications to mechanical and electrical systems

Week 9: Applications: Stable adaptive control - Estimation, indirect, and direct adaptive control

Week 10: Applications: Lyapunov function theory for control problems - General form, specialization to linear systems, linearization, and cascade systems

Week 11: Applications: Optimal control and inverse optimality

Week 12: Applications: Model predictive control

Instructor bio

Prof. Vijaysekhar Chellaboina

IIT Madras

Professor Vijaysekhar Chellaboina received his B. Tech and M.S. in mechanical engineering at the Indian Institute of Technology, Madras (Chennai, India) and the Florida Institute of Technology (Melbourne, FL, USA). He received his Ph.D. from the Georgia Institute of Technology (Atlanta, GA, USA), specializing in the mathematical theory of nonlinear control systems. Professor Vijay’s archival contributions include over 200 journals, peer-reviewed conference articles, and five books (published by Springer and Princeton University Press). His book on nonlinear dynamical systems is used as a textbook/reference in advanced courses at top universities worldwide. His research interests are in stability theory and feedback control applications to complex systems, including biomedical and financial systems. His teaching experience includes courses in mechanical and electrical engineering and mathematics.

Professor Vijaysekhar Chellaboina is currently Dean of Computer Science at UPES and an adjunct professor of Electrical Engineering at IIT Madras. Before joining UPES, Professor Vijay was a faculty member at the Universities of Missouri and Tennessee, and Mahindra University. He also served as Dean at Mahindra, SRM, and GITAM universities. In addition, he was a principal scientist at TCS Research, heading the risk and finance group.

More details may be found at the following links.

https://www.linkedin.com/in/vchellaboina/

https://scholar.google.co.in/citations?user=WPy-V3EAAAAJ&hl=en

Course certificate

The course is free to enroll and learn from. But if you want a certificate, you have to register and write the proctored exam conducted by us in person at any of the designated exam centres.
The exam is optional for a fee of Rs 1000/- (Rupees one thousand only).
Date and Time of Exams: 27 October 2024 Morning session 9am to 12 noon; Afternoon Session 2pm to 5pm.
Registration url: Announcements will be made when the registration form is open for registrations.
The online registration form has to be filled and the certification exam fee needs to be paid. More details will be made available when the exam registration form is published. If there are any changes, it will be mentioned then.
Please check the form for more details on the cities where the exams will be held, the conditions you agree to when you fill the form etc.

CRITERIA TO GET A CERTIFICATE

Average assignment score = 25% of average of best 8 assignments out of the total 12 assignments given in the course.
Exam score = 75% of the proctored certification exam score out of 100

Final score = Average assignment score + Exam score

YOU WILL BE ELIGIBLE FOR A CERTIFICATE ONLY IF AVERAGE ASSIGNMENT SCORE >=10/25 AND EXAM SCORE >= 30/75. If one of the 2 criteria is not met, you will not get the certificate even if the Final score >= 40/100.

Certificate will have your name, photograph and the score in the final exam with the breakup.It will have the logos of NPTEL and IIT Madras .It will be e-verifiable at nptel.ac.in/noc.

Only the e-certificate will be made available. Hard copies will not be dispatched.

Once again, thanks for your interest in our online courses and certification. Happy learning.

- NPTEL team

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