Nonlinear Control Design

By Prof. Srikant Sukumar | IIT Bombay

Learners enrolled: 253 | Exam registration: 13

ABOUT THE COURSE:

Nonlinear systems are ubiquitous and therefore their study and control design are prevalent in the control engineering community. This course will focus on, by now, classical methods for control design of nonlinear systems. We introduce the Lyapunov theorems in brief to enable us to analyze the stability of the closed-loop systems involved. Design methods such as Backstepping, Passivity based design and feedback linearization will be looked at in detail. The course will be interspersed with examples from aero-mechanical systems such as ground/aerial robots, spacecraft attitude dynamics and so on. We will end with some advanced design methods for state constrained control and adaptive control. This course will be of interest to junior/senior researchers in advanced tech like drones, autonomous cars, Launch vehicle control, aerospace control, smart grid systems, battery electric vehicles and so on.

INTENDED AUDIENCE: Senior undergraduates, graduate students

PREREQUISITES: Linear Systems – background in state space dynamical systems

INDUSTRY SUPPORT: Mathworks, John Deere, Mercedes Benz research, Defense research agencies, ISRO

Summary

Course Status :	Completed
Course Type :	Core
Language for course content :	English
Duration :	12 weeks
Category :	Mechanical Engineering
Credit Points :	3
Level :	Postgraduate
Start Date :	22 Jan 2024
End Date :	12 Apr 2024
Enrollment Ends :	05 Feb 2024
Exam Registration Ends :	16 Feb 2024
Exam Date :	28 Apr 2024 IST

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

Page Visits

Course layout

Week 1 : Nonlinear Systems Examples, Existence and Uniqueness of Solutions; Common myths in control; Vector, Matrix and Signal Norms

Week 2 : Lyapunov Stability definitions – stability, uniformity, attractivity, asymptotic stability, exponential stability; Stability of Linear systems.

Week 3 : Function classes; Definiteness, radial boundedness, decrescence; Lyapunov stability theorems

Week 4 : Proof of stability theorems – Stability in the sense of Lyapunov and Asymptotic Stability

Week 5 : La Salle’s Invariance principle; Krasovskii-Barbashin-LaSalle stability theorems; Proof of LaSalle’s invariance principle, worked out examples

Week 6 : Control Lyapunov Functions; Small Control Property;

Week 7 : Arstein Sontag Universal Controller; Backstepping method for control design, integrator backstepping

Week 8 : Passivity based control design – input-output passivity, feedback passivation, spacecraft attitude control example

Week 9 : Feedback linearization – motivation, Lie derivatives, relative degree results, Diffeomorphism coordinate transformation

Week 10 : Feedback linearization – Zero dynamics, local Asymptotic Stability, Frobenius theorem with proof, integrable distributions, examples.

Week 11 : Advanced Design Methods – Constrained control via Barrier functions, Adaptive control

Week 12 : Advanced design methods – Finite Time Control, Sliding Mode Control.

Books and references

1. H. K. Khalil, Nonlinear Systems, Pearson Publications, Third Edition, 2002
2. M. Vidyasagar, Nonlinear Systems Analysis, Second Edition, SIAM, 2002
3. Miroslav Krstic, Ioannis Kanellakopoulos, Petar V. Kokotovic Nonlinear and Adaptive Control Design, Wiley Series, July 1995

Instructor bio

Prof. Srikant Sukumar

IIT Bombay

Prof. Srikant Sukumar completed his PhD in Aerospace Engineering from The University of Texas at Austin with a specialisation in nonlinear adaptive control of space and aerial vehicles in 2011. He has since been a faculty at the Systems and Control Engineering Department at IIT Bombay where he is currently an Associate Professor. He has been a Max Planck Fellow. He serves as a member of the IEEE conference editorial board , the IEEE Technical Society for Space Vehicles and as an Associate Editor for the IEEE Transactions for Aerospace Engineering Systems. He actively mentors student teams in developing urban aerial vehicles, nano-satellites and autonomous vehicles. His research interests lie in adaptive nonlinear control, geometric control and observation, cooperative control and estimation over networks.

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: 28 April 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 Bombay .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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