First cycle
degree courses
Second cycle
degree courses
Single cycle
degree courses
School of Engineering
Course unit
INP4063840, A.A. 2019/20

Information concerning the students who enrolled in A.Y. 2018/19

Information on the course unit
Degree course Second cycle degree in
IN0527, Degree course structure A.Y. 2008/09, A.Y. 2019/20
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Number of ECTS credits allocated 6.0
Type of assessment Mark
Course unit English denomination ADVANCED TOPICS IN CONTROL
Department of reference Department of Information Engineering
E-Learning website
Mandatory attendance No
Language of instruction English
Single Course unit The Course unit can be attended under the option Single Course unit attendance
Optional Course unit The Course unit can be chosen as Optional Course unit

Teacher in charge FRANCESCO TICOZZI ING-INF/04

ECTS: details
Type Scientific-Disciplinary Sector Credits allocated
Core courses ING-INF/04 Automatics 6.0

Course unit organization
Period Second semester
Year 2nd Year
Teaching method frontal

Type of hours Credits Teaching
Hours of
Individual study
Lecture 6.0 48 102.0 No turn

Start of activities 02/03/2020
End of activities 12/06/2020
Show course schedule 2019/20 Reg.2008 course timetable

Examination board
Board From To Members of the board
4 A.A. 2018/2019 01/10/2018 15/03/2020 TICOZZI FRANCESCO (Presidente)
FERRANTE AUGUSTO (Membro Effettivo)
ZORZI MATTIA (Supplente)

Prerequisites: The knowledge of the material presented in the courses "Systems and models", "automatic control" and "linear system theory" is a prerequisite.
Target skills and knowledge: The course aims to provide the student with the following competences and skills:

- Know the main classes of nonlinear systems and how these have different behaviors with respect to the linear models they have seen in previous courses;
- Know the language and the mathematical techniques used in the study of stability of nonlinear systems, also in the varying case, for both equilibria and more general sets;
- Know how to tackle a stabilization problem and design a stabilizing feedback law using Lyapunov control functions;
- Acquire familiarity with the language of differential geometry and the study of dynamical systems on manifolds;
- Know the basic concepts and definitions of controllability in the geometric approach;
- Know the methods for exact linearization, the conditions for the existence of linearizing feedback laws, and the design methods for stabilizing control law on the linearized systems.
Examination methods: The evaluation of the knowledge and skills acquired is done by:

1) During the course, assigning and evaluating homeworks that are graded by the instructor and contribute to the final evaluation;
This allows to evaluate timely and in detail the learning advancement regarding both the basic notions and the design of control laws.

2) through the assignment of a final project, in which students employ the knowledge and abilities they acquired in the study and presentation to the class of a new topic, or a design problem. This allows for the evaluation of both the ability to apply what has been learned to a new topic and the proficiency in explaining what has been done.
Assessment criteria: The evaluation criteria that will be employed:

1) Completeness of the acquired knowledge;
2) Ability to properly use the acquired mathematical and technical language;
3) Level of of confidence in mastering the concepts acquired in the course;
4) Effectiveness of the presentation and communication of the methods used;
5) Methodological rigor in the derivation of the results;
Course unit contents: The course will cover:

1) Qualitative analysis of nonlinear systems and comparison with linear systems. Existence and uniqueness of solutions and fundamental properties. Classes of nonlinear systems;

2) Lyapunov stability theory, for both time invariant and time varying systems. Invariance principle and Barbalat's lemma for the stability of sets. Lyapunov's control functions and design of stabilizing feedback laws.

3) Elements of differential geometry: manifolds, tangent space, vector fields and dynamics on manifolds. Invariant manifolds of an equilibrium, center manifold and reduction principle.

4) Elements of geometric control, switching systems, Lie brackets and accessibility. Controllability of nonlinear systems.

5) Exact linearization techniques. Normal form and relative degree of control-affine systems. Control and stabilization via feedback linearization.
Planned learning activities and teaching methods: The course will consists of classroom lectures on theory and applications, and will be integrated by homework assignments and students presentations. In addition, the design techniques presented in the classroom will be tested in the automation laboratory, applying them to a balancing robot.
Additional notes about suggested reading: Instructor's lecture notes, which cover the full course, and additional material will be made available on the elearning course website. The notes are also available in print at the Progetto bookstore in Padova.
Textbooks (and optional supplementary readings)
  • Hassan K. Khalil, Nonlinear Systems. Upper Saddle River, NJ: Prentice Hall, 2002. Cerca nel catalogo

Innovative teaching methods: Teaching and learning strategies
  • Lecturing
  • Laboratory
  • Problem solving
  • Flipped classroom

Innovative teaching methods: Software or applications used
  • Moodle (files, quizzes, workshops, ...)
  • One Note (digital ink)
  • Matlab