Schedule: Monday, Wednesday, Friday 9:30am-10:18am 135
Caldwell Labs .
This is a new graduate course within the control
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
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
Textbook and useful
- H.H Khalil, Nonlinear
Systems (3rd edition), Prentice Hall, 2002.
(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).
- 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 Input-to-State Stability
- E.D. Sontag, "Smooth Stabilization Implies Coprime
- A.J. van der Schaft, "L2-Gain Analysis of Nonlinear
Systems, and Nonlinear State Feedback H_inf Control"
- C.I. Byrnes, A. Isidori, J.C. Willems,
Feedback Equivalence, and the Global Stabilization of Minimum Phase
- A.R. Teel, "Feedback Stabilization of Nonlinear
Systems: Results Based on L_inf
- C.I. Byrnes and A. Isidori, "Asymptotic
stabilization of minimum phase nonlinear systems"
- A. Isidori and C.I. Byrnes, "Output regulation of
Grading: Homework 40% , Take-home final (Project) 60%.
- Input-Output and Input-to-State stability
of nonlinear systems. Sontag's input-to-state stability. Definitions
and Lyapunov-like characterizations. Feedback equivalence and
input-to-state stabilizability of nonlinear systems. Input-to-state
stability of cascade systems. Design examples.
- Dissipative systems. L2 - gain and
passivity theory. Dissipative and zero-state detectable
systems. Finite L2-gain systems, and associated small-gain theorem.
Passive systems and passive interconnections. Feedback equivalence to a
passive systems. Examples.
- Stability of interconnected nonlinear
systems. The small-gain theorem for ISS systems. Robust
- Global stabilization for nonlinear systems
in normal form. Backstepping techniques. Control Lyapunov functions.
stabilization of nonlinear systems in normal form. Bacciotti's
theorem on "potentially global" stabilization. The peaking phenomenon.
Robust semi-global stabilization: the Teel-Praly construction. Design
- Tracking and regulation
in nonlinear systems: the Isidori-Byrnes regulator. Examples
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