Nonlinear Control Systems
IST-DEEC PhD Course - Springer Semester 2011/2012
Posted on May 15, 2012
The homework #8 [HW#8] has been posted online.
The due date is Monday, May 21, 2012.
Posted on May 7, 2012
The homework #7 [HW#7] has been posted online.
The due date is Monday, May 14.
The slides of part 7- Feedback Linearization can be downloaded here [Slides#7]
Posted on April 24, 2012
The homework #6 [HW#6] has been posted online.
The due date is Wednesday, May 2.
The slides of part 6- Nonlinear Design can be downloaded here [Slides#6]
Posted on April 2, 2012
The homework #5 [HW#5] has been posted online.
The due date is Wednesday, April 11.
The slides of part 5- Input-Output Stability can be downloaded here [Slides#5]
Posted on March 23, 2012
The homework #4 [HW#4] has been posted online.
The due date is Wednesday, March 28.
Posted on March 14, 2012
The homework #3 [HW#3] has been posted online.
The due date is Wednesday, March 21.
Posted on March 8, 2012
The slides of part 3- Fundamental properties can be downloaded here [Slides#3]
The slides of part 4- Lyapunov stability can be downloaded here [Slides#4]
The homework #2 [HW#2] has been posted online.
The due date is Wednesday, March 14.
Posted on March 2, 2012
The slides of part 1- Introduction to Nonlinear Systems can be downloaded here [Slides#1]
The slides of part 2- Mathematical review can be downloaded here [Slides#2]
The homework #1 [HW#1] has been posted online.
The due date is Monday, March 12.
Monday 16:00 – 17:30 room C10
Wednesday 16:00 – 17:30 room E1
Computer simulation of an autonomous underwater vehicle following a desired 3D trajectory
The main goal of this course is to provide to the students a solid background in analysis and design of nonlinear control systems.
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.
Basic knowledge of calculus, linear algebra and ordinary differential equations is assumed.
Mondays – 16h00-17h30 room C10
Wednesdays – 16h00-17h30 room E1
· Antonio Pedro Aguiar
Office: 8.13, North Tower, IST
Phone: +351 21 841 8056
Office Hours: Please email or phone in advance to schedule an appointment.
Main: Khalil, H. K. Nonlinear Systems, 3rd Edition, Prentice Hall, Upper Saddle River, NJ, 2002.
Complementary: Collection of journal papers.
Homeworks – 30%
Final Project – 40%
Final Exam – 30% (24h take home)
The following two types of projects are possible in this course:
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
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.
3 hours/week (theoretical lectures)