EEL 824, I semester 2014-15
This is the the webpage for EEL 824, I semester 2014-15
Nonlinear Systems
Instructor
Shaunak Sen
E-mail: shaunak.sen@ee.iitd.ac.in
Lectures: MTh 5:00-6:20pm
Room: Block II - 336
Announcements
21.11.2014: MAJOR TEST scheduled from 3:30PM-5:30PM on Sun, 23.11.2014 in III-386. Please check Exam Schedule for up-to-date information.
14.10.2014: MINOR TEST 2 solutions posted.
07.10.2014: HW2 solutions posted.
07.10.2014: MINOR TEST 2 scheduled from 7-8PM on Wed, 08.10.2014 in III-374. Please check Exam Schedule for up-to-date information.
24.09.2014: Project guidelines posted here.
12.09.2014: HW2 posted.
08.09.2014: MINOR TEST 1 solutions posted.
29.08.2014: HW1 solutions posted.
22.08.2014: MINOR TEST 1 scheduled from 7-8PM on Sun, 31.08.2014 in III-374. Please check Exam Schedule for up-to-date information.
22.08.2014: HW1 posted.
24.07.2014: Webpage online.
Lectures
| S. No. | Date | Topic | Suggested Reading | Homework |
| 1 | Week 1
(Jul 25) | Introduction to Dynamics
Existence & Uniqueness
Phase Plane Analysis | Strogatz 1
Slotine & Li 1 | |
| 2 | Week 2
(Jul 28, 31) | Linear Systems
Classification of Equilibria | Strogatz 5.1-5.2, 6.1-6.2
Lecture_Jul28 | |
| 3 | Week 3
(Aug 4, 7) | Linearization
Stable & unstable manifolds
Limit Cycles & Oscillations | Strogatz 6.3-6.4
Lecture_Aug4
Strogatz 7.0
Lecture_Aug7 | |
| 4 | Week 4
(Aug 11, 13) | van der Pol oscillator
Poincare-Bendixson Theorem
Bifurcations
Saddle-node | Strogatz 7.1-7.2
Strogatz 8.0-8.1
Lecture_Aug11
Lecture_Aug13 | |
| 5 | Week 5
(Aug 21) | Pitchfork, Transcritical
Hopf | Strogatz 8.1-8.2
Lecture_Aug21 | HW1
Solutions |
| 6 | Week 6
(Aug 25,
Aug 31 - MINOR TEST 1) | Lyapunov Stability
Positive definite functions | Lecture_Aug25
Optional: Slotine & Li 3.4-3.4.1 | |
| 7 | Week 7
(Sep 1, 4) | Stability definitions
Lyapunov's Theorem | Lecture_Sep1
Lecture_Sep4
Optional: Slotine & Li 3.1-3.2,
Slotine & Li 3.4.2, 3.6 | |
| 8 | Week 8
(Sep 8, 11) | La Salle's Invariance Principle
Passivity | Optional: Slotine & Li 3.4.3,
Khalil Ch 6 | HW2
Solutions |
| 9 | Week 9
(Sep 15, 18) | Circle Criterion
Nonlinear Control Overview | Optional: Slotine & Li 4.7-4.8 | |
| 10 | Week 10
(Sep 22, 25) | Feedback Linearization
Examples, Internal Dynamics | Optional: Slotine & Li Ch. 6.1.1-6.1.3 | |
| 11 | Week 11
(Sep 29) | Lie Derivatives, Lie Brackets | Optional: Slotine & Li 6.2 | |
| 12 | Week 12
(Oct 8 - MINOR TEST 2) | | | |
| 13 | Week 13
(Oct 13, 16) | Input-State Linearization | Optional: Slotine & Li 6.3 | |
| 14 | Week 14
(Mid-Semester Break) | | | |
| 15 | Week 15
(Oct 27, 30) | Sliding Control | Optional: Slotine & Li 7.1.1, 7.1.3 | |
| 16 | Week 16
(Nov 3
Nov 8 - Projects) | Perturbation | Optional: Khalil Ch. 10 | |
| 17 | Week 17
(Nov 10, 13) | Singular Perturbation
Describing Functions | Optional: Khalil Ch. 11
Optional Slotine & Li Ch. 5 | |
| 18 | Week 18
(Nov 17) | Input-Output Approximation
Limit Cycle Estimation | |
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Reference Textbooks
S. Strogatz, Nonlinear Dynamics And Chaos, Westview Press, 1994. ISBN: 978 — 0738204536
J. E. Slotine & W. Li, Applied Nonlinear Control, Prentice Hall, 1991. ISBN: 0-13-040890-5
H. Khalil, Nonlinear Systems, Prentice Hall; 3rd edition, 2001. ISBN: 978 — 0130673893
M. Vidyasagar, Nonlinear Systems Analysis, Society for Industrial and Applied Mathematics, 2002. ISBN 0898715261
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