Course
Schedule: Monday, Wednesday, Friday 9:30am10:18am 135
Caldwell Labs .
This is a new graduate course within the control
area.
It aims at providing the necessary background for advanced analysis and
control of nonlinear systems. The course will emphasize recent
as well as classical techniques and methodologies for designing control
systems for complex,
interconnected nonlinear systems. Classical results in the
stabilization
of nonlinear systems will also be treated in detail. Applications of
nonlinear control design ranging from aerospace to robotics will be
considered throughout the course.
Prerequisites: EE 754
Nonlinear systems.
Textbook and useful
references:
 H.H Khalil, Nonlinear
Systems (3rd edition), Prentice Hall, 2002.
 A. Isidori, Nonlinear
Control Systems II, Springer Verlag, 1999.
 A. Isidori, Nonlinear
Control Systems I (3rd edition), Springer Verlag, 1996.
 E.D. Sontag, Mathematical
control theory : deterministic finite dimensional systems (2nd
edition), Springer Verlag, 1998.
 Selected papers may include
(but not limited to):
 E.D. Sontag, "On the InputtoState Stability
Property"
 E.D. Sontag, "Smooth Stabilization Implies Coprime
Factorization"
 A.J. van der Schaft, "L2Gain Analysis of Nonlinear
Systems, and Nonlinear State Feedback H_inf Control"
 C.I. Byrnes, A. Isidori, J.C. Willems,
"Passivity,
Feedback Equivalence, and the Global Stabilization of Minimum Phase
Nonlinear Systems"
 A.R. Teel, "Feedback Stabilization of Nonlinear
Systems: Results Based on L_inf
Inputoutput Stability"
 C.I. Byrnes and A. Isidori, "Asymptotic
stabilization of minimum phase nonlinear systems"
 A. Isidori and C.I. Byrnes, "Output regulation of
nonlinear systems"
(PLEASE NOTE: Although no
official textbook will be followed in this course, the book by Khalil
can be used to
cover large portions of the material. Notes and selected journal
papers will be made available throughout the course).
Grading: Homework 40% , Takehome final (Project) 60%.
Course outline 

 InputOutput and InputtoState stability
of nonlinear systems. Sontag's inputtostate stability. Definitions
and Lyapunovlike characterizations. Feedback equivalence and
inputtostate stabilizability of nonlinear systems. Inputtostate
stability of cascade systems. Design examples.

 Dissipative systems. L2  gain and
passivity theory. Dissipative and zerostate detectable
systems. Finite L2gain systems, and associated smallgain theorem.
Passive systems and passive interconnections. Feedback equivalence to a
passive systems. Examples.

 Stability of interconnected nonlinear
systems. The smallgain theorem for ISS systems. Robust
stabilization. Design
examples.

 Global stabilization for nonlinear systems
in normal form. Backstepping techniques. Control Lyapunov functions.
SontagArtstein formula.

 Semiglobal
stabilization of nonlinear systems in normal form. Bacciotti's
theorem on "potentially global" stabilization. The peaking phenomenon.
Robust semiglobal stabilization: the TeelPraly construction. Design
examples.

 Tracking and regulation
in nonlinear systems: the IsidoriByrnes regulator. Examples

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