18-879 PR/T: Nonlinear Control Systems
IST/CMU PhD Course - Springer Semester 2011
|
Computer simulation of an autonomous
underwater vehicle following a desired 3D trajectory |
Announcements
Posted on April 12, 2011
The slides of part “10 – Adaptive nonlinear control (a
simple example)” can be downloaded here [Slides#10].
Posted on April 12, 2011
The slides of part “9 – Advanced Stability Analysis” can be downloaded here [Slides#9].
Homework #11 can be downloaded here [HW#11].
Posted on March 31, 2011
The last version of part “8 – Passivity” can be downloaded here [Slides#8_v3].
Homework #10 can be downloaded here [HW#10].
Posted on March 31, 2011
The second version of part “8 – Passivity” can be downloaded here [Slides#8_v2].
Homework #9 can be downloaded here [HW#9].
Posted on March 24, 2011
The last version of the slides of
part “7 – Feedback Linearization” and the
first version of part “8 – Passivity” can be downloaded here [Slides#7_v4],
[Slides#8_v1].
Posted on March 22, 2011
The third version of the slides of part “7 – Feedback Linearization” can be downloaded here [Slides#7_v3].
Homework #8 can be downloaded here [HW#8].
Posted on March 17, 2011
The second version of the slides of
part “7 – Feedback Linearization” can be downloaded here [Slides#7_v2].
Posted on March 15, 2011
The first set of slides of part “7
– Feedback Linearization” can be downloaded here [Slides#7_v1].
Posted on March 3, 2011
The slides about a Lyapunov based design control law for a Hovercraft can be downloaded here [Slides#6_Hovercraft].
Posted on March 3, 2011
Homeworks #6 and #7 can be
downloaded here [HW#6]
[HW#7].
The due date of both homeworks is Tuesday, March 15th.
Posted on February 28, 2011
The second version of part “6 -
Nonlinear Design” can be downloaded here [Slides#6_v2].
Posted on February 21, 2011
The first set of slides of part “6 -
Nonlinear Design” can be downloaded here [Slides#6_v1].
Posted on February 20, 2011
The 24h take home exam will be on
April 28th.
Regarding the project, the following
two types of projects are possible in this course:
1. Solution of a research problem
relevant to the student’s area of research, which makes use of methods
described in the course.
2. Independent study of a topic not
covered in-depth in class (e.g., reading a paper or book chapter).
If you need suggestions just come to
speak with me or Sergio.
You should define a project no
longer than March 18th. Please send an email to me and Sergio
describing what you plan to do.
The final presentation is required
in class during the days 3 and 5 of May and they should have a maximum of 8
minutes + 2 min. of questions that can arise from me, Sergio
or your colleagues.
You should deliver on the day of
your presentation a final report no longer then 5 pages plus a copy of the
slides of your presentation.
Posted on February 20, 2011
The homework #5 [HW#5] has been posted online.
The due date is Tuesday, March 1st.
Posted on February 14, 2011
The slides of “5- Input-Output Stability” can be
downloaded here [Slides#5].
Posted on February 12, 2011
The due date of homework #4 [HW#4] has been postponed to February 22nd.
Posted on January 31, 2011
The last version of part “4-
Lyapunov Stability” can be downloaded here [Slides#4_v4].
Posted on February 1, 2011
The homework #3 [HW#3] has been posted online.
The due date is next Tuesday (Feb.
8th).
Posted on January 31, 2011
Version 3 of part “4- Lyapunov
Stability” can be downloaded here [Slides#4_v3].
Posted on January 26, 2011
Version 2 of part “4- Lyapunov
Stability” can be downloaded here [Slides#4_v2].
Posted on January 25, 2011
The homework #2 [HW#2] has been posted online.
The due date is next Tuesday (Feb.
1st).
Posted on January 19, 2011
The first 28 slides of part “4- Lyapunov Stability” can be downloaded here [Slides#4].
Posted on January 18, 2011
The homework #1 [HW#1] has been posted online.
The due date is next Tuesday (Jan.
25).
Posted on January 16, 2011
The third part “3- Fundamental
properties” can be downloaded here [Slides#3].
Posted on January 12, 2011
The second part “2- Mathematical review” can be downloaded here [Slides#2].
Posted on January 11, 2011
The slides of chapter “1-
Introduction to Nonlinear Systems” can be downloaded here [Slides#1].
Posted on January 5, 2011
Schedule: (First lecture: Tuesday,
January 11, 2011)
Tuesday 14:00
– 15:30 (Lisbon time) 9:00
– 10:30 (Pittsburgh time)
Thursday 14:00
– 15:30 (Lisbon time) 9:00
– 10:30 (Pittsburgh time)
Location:
IST: Institute
for Systems and Robotics (ISR)Videoconference Room,
7th floor, North Tower, IST.
CMU: INI
building, Henry Street.
Objective
The main goal of this course is to provide to the students a
solid background in analysis and design of nonlinear control systems.
Course
Description
Many control systems of practical importance are
inherently nonlinear. A common practice for control system design is to
linearize the system to be controlled around some equilibrium or operating
point through small perturbation state approximations. The key assumption is
that the range of operation is restricted to a small region around the
equilibrium on which the linear model remains valid. As a consequence, adequate
control is only guaranteed in a neighborhood of the selected operating points.
Moreover, performance can suffer significantly when the required operating
range is large, such as when controlling an autonomous vehicle that executes
maneuvers that emphasize its nonlinearity and cross-couplings.
This course covers the analysis and design of
nonlinear control systems and is suitable for post-graduate students in science
and engineering. The course begins with an introduction to nonlinear system
theory and stability analysis. Topics include Lyapunov stability analysis
techniques, stability of perturbed systems with vanishing and non-vanishing
perturbations, input-to-state stability, input-output stability and passivity.
The last part of the course is dedicated to nonlinear control design tools such
as feedback linearization, sliding mode control, Lyapunov redesign,
backstepping, passivity based control and nonlinear adaptive control (if time
permits). Emphasis is placed upon application of the theory to systems of
interest to the students.
Prerequisites
Basic
knowledge of calculus, linear algebra and ordinary differential equations is
assumed.
Class
Schedule
Tuesdays
and Thursdays, 9 a.m.-10:30 a.m.
Course
Personnel
Instructor:
·
Antonio Pedro Aguiar
Office: 8.13,
North Tower, IST, Lisbon
Phone: +351 21 841 8056
Email: pedro@isr.ist.utl.pt
Web: http://users.isr.ist.utl.pt/~pedro/
Office Hours: Please email or phone in advance to schedule an appointment.
Teaching Assistants:
·
Sérgio Daniel Pequito
Office: B21
(Potter Hall)
Phone:
Email: spequito@andrew.cmu.edu
Office Hours: Please email or phone in advance to schedule an appointment.
Course Management Assistant:
· Bara Ammoura
Hamerschalg Hall D200
412-268-6595
Office Hours: Monday-Friday, 8:30 a.m.-5:00p.m.
Textbook
Khalil,
H. K. Nonlinear Systems, 3rd Edition, Prentice Hall, Upper Saddle River, NJ,
2002.
Grading
Policy
Homeworks
– 30%
Final
Project – 40%
Final
Exam – 30% (24h take home)
Projects
The following
two types of projects are possible in this course:
- Solution of a research problem
relevant to the student’s area of research, which makes use of methods
described in the course.
- Independent study of a topic
not covered in-depth in class (e.g., reading a paper or book chapter).
Course
Topics
1. Introduction to nonlinear systems
Nonlinear systems vs. linear systems, multiple isolated equilibrium
points, finite escape times, limit cycles.
2. Mathematical preliminaries
Normed vector spaces. Induced norms. Mean value and implicit function theorems.
Gronwall-Bellman inequality. Lipschitz condition.
3. Fundamental
properties
Local and global existence and uniqueness of
solutions. Continuity with
respect to initial conditions. Comparison Principle.
4. Lyapunov Stability
Autonomous
Systems. The Invariance Principle. Linear Systems and
Linearization. Comparison Functions. Nonautonomous Systems. Linear Time-Varying
Systems and Linearization. Converse Theorems. Boundedness and
Ultimate Boundedness. Input-to-State Stability.
5. Input–Output Stability
L Stability. L Stability of State Models. L2
Gain. Feedback Systems: The Small-Gain Theorem
6. Passivity
Memoryless Functions. State Models. Positive Real
Transfer Functions. L2 and Lyapunov Stability. Feedback Systems: Passivity
Theorems.
7. Frequency Domain Analysis of Feedback Systems
Absolute Stability: Circle Criterion, Popov Criterion.
8. Advanced Stability Analysis
The Center Manifold Theorem. Region of Attraction.
Invariance-like Theorems. Stability of Periodic Solutions
9. Stability of Perturbed Systems
Vanishing Perturbation. Nonvanishing Perturbation. Comparison Method.
10. Feedback Linearization
Motivation. Input–Output Linearization.
Full-State Linearization. State Feedback Control.
Stabilization. Tracking.
11. Nonlinear Design Tools
Sliding Mode Control: Motivating Example, Stabilization, Tracking, Regulation via Integral Control. Lyapunov Redesign:
Stabilization, Nonlinear Damping. Backstepping. Passivity-Based Control. Basic nonlinear adaptive control design.