ENEE 661 - Nonlinear Control Systems (P. S. Krishnaprasad)
ENEE 661 - Nonlinear Control Systems
Spring 2020
Last Update: Wednesday January 15, 2020
Course Information
Special Announcements (weekly)
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Lecture Notes by P. S. Krishnaprasad (LaTeX version)
Survey Lecture (on some aspects of geometric control theory)
Correction to pages 30-31 of Lecture 4 on flow expression
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Supporting References (papers, books)
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Homework Assignments Spring 2017
Problem Set 1
Problem Set 2
Problem Set 3
Problem Set 4
Problem Set 5
Problem Set 6
Problem Set 7
Problem Set 8
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Older Hand-written Weekly Lecture Notes by P. S. Krishnaprasad
Lecture 1(a) (Introducing nonlinear control systems) Lecture 1(b) (Frenet-Serret framing of curves and control on SE(3))
Lecture 1(c) (natural framing of curves and control on SE(3))
Lecture 2(a) (matrix Lie groups and Lie algebras - very basic introduction)
Lecture 2(b) (Lie brackets in control - examples)
Lecture 3(a) (contraction mappings, fixed points,
existence and uniqueness of solutions to ODE's) Lecture 3(b) (mean value theorem)
Lecture 4 (planar systems, Hartman-Grobman theorem, Poincare-Bendixson theorem)
Lecture 5 (on Index) Lecture 5 continued (more on Index)
Lecture 6 Lyapunov and Lasalle Theorems; Chetaev Theorem; Region of attraction
Lecture 7 Lyapunov theorems for time-varying systems; Linearization Theorems (stability) and Linearization Theorems (instability)
Lecture 8 Feedback stabilization; feedback linearization
Lecture 9 Stability theory: input-output aspects
Lecture 10 Passivity and Absolute Stability
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Older Homework Assignments
Problem Set 1
Problem Set 2
Problem Set 3 (part 1) part 2
Problem Set 4
Problem Sets 5, 6 and 7
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Homework solutions are sent by email
For Matlab problems remember to include your code.
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Examinations
Mid Term I
Mid Term II
Final
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Other Resources (OR)
My lecture notes on Optimal Control (ENEE 664)
My lecture notes on (Linear) System Theory (ENEE 660)
Website for Feedback Systems: An Introduction for Scientists and Engineers by K. J. Astrom and R. M. Murray On-line readable book
Motion, Control and Geometry Four expository articles illustrating nonlinear control in action
Real Analysis Book by Cinlar and Vanderbei - material useful in Systems courses published by Springer in Undergraduate Texts in
Mathematics Series as Real and Convex Analysis (recommended)
About Sophus Lie
About Stefan Banach
About A. M. Lyapunov
About G. D. Birkhoff