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B028294 - NONLINEAR DYNAMICAL SYSTEMS
Main information
Teaching Language
Course Content
Suggested readings
Learning Objectives
Teaching Methods
Type of Assessment
Course program
Academic Year 2021-22
Course year
Second year - First Semester
Belonging Department
Information Engineering (DINFO)
Modulo di sola Frequenza of
Scientific Area
ING-INF/04 - SYSTEMS AND CONTROL ENGINEERING
Credits
6
Teaching Hours
48
Teaching Term
13/09/2021 ⇒ 17/12/2021
Attendance required
No
Type of Evaluation
Giudizio Finale
Course Content
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Course program
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Lectureship
Mutuality
Course teached as:
B024387 - SISTEMI DINAMICI NON LINEARI
Second Cycle Degree in ELECTRICAL AND AUTOMATION ENGINEERING
Curriculum INGEGNERIA ELETTRICA
B024387 - SISTEMI DINAMICI NON LINEARI
Second Cycle Degree in ELECTRICAL AND AUTOMATION ENGINEERING
Curriculum INGEGNERIA ELETTRICA
Teaching Language
Italian
Course Content
The module introduces the main techniques for internal and external stability analysis of nonlinear dynamical systems. The main topis deal with: Lyapunov stability, ISS stability, dissipativity and monotone systems.
Suggested readings (Search our library's catalogue)
- Lecture Notes
[1] A. Isidori, Nonlinear Control Systems, Springer-Verlag, London, 1989.
[2] A. Isidori, Nonlinear Control Systems II, Springer-Verlag, London, 1999.
[3] H. Khalil, Nonlinear systems, Prentice Hall, 2001.
[4] M. Kristic, I. Kanellakopoulos and P.V. Kokotovic, Nonlinear and adaptive control design, Wiley, 1995.
[5] R. Lozano, B. Brogliato, O. Egeland and B. Maschke, Dissipative systems analysis and control, Springer-Verlag, 2000.
[6] S. Sastry, Nonlinear Systems,Interdisciplinary Applied Mathematics,
Springer, 1999.
[7] J.J Slotine and W. Li, Applied Nonlinear Control, Prentice-Hall, 1991.
[8] E.D. Sontag, Mathematical Control Theory, Texts in Applied Mathematics
6, Springer, 1998.
[9] A.J. van der Schaft, L2-Gain and Passivity Techniques in Nonlinear Control, Springer-Verlag, London, 1999.
[1] A. Isidori, Nonlinear Control Systems, Springer-Verlag, London, 1989.
[2] A. Isidori, Nonlinear Control Systems II, Springer-Verlag, London, 1999.
[3] H. Khalil, Nonlinear systems, Prentice Hall, 2001.
[4] M. Kristic, I. Kanellakopoulos and P.V. Kokotovic, Nonlinear and adaptive control design, Wiley, 1995.
[5] R. Lozano, B. Brogliato, O. Egeland and B. Maschke, Dissipative systems analysis and control, Springer-Verlag, 2000.
[6] S. Sastry, Nonlinear Systems,Interdisciplinary Applied Mathematics,
Springer, 1999.
[7] J.J Slotine and W. Li, Applied Nonlinear Control, Prentice-Hall, 1991.
[8] E.D. Sontag, Mathematical Control Theory, Texts in Applied Mathematics
6, Springer, 1998.
[9] A.J. van der Schaft, L2-Gain and Passivity Techniques in Nonlinear Control, Springer-Verlag, London, 1999.
Learning Objectives
- Understanding of advantages and technical difficulties entailed in the adoption of nonlinear dynamical models
-Understanding of local and global analysis techniques for nonlinear systems
-Understanding robustness with respect to exogenous disturbances
-Understanding of local and global analysis techniques for nonlinear systems
-Understanding robustness with respect to exogenous disturbances
Teaching Methods
Frontal classes, both with theory and examples
Type of Assessment
Oral examination:
- ability to explain the concepts discussed in the module
- ability to explain the theorems and technical results as well as their implications
- ability to solve examples and exercises related to the concepts discussed in the module
- ability to explain the concepts discussed in the module
- ability to explain the theorems and technical results as well as their implications
- ability to solve examples and exercises related to the concepts discussed in the module
Course program
-Introduction to nonlinear systems, motivations and notations
-Nonlinear dynamical system in dimension 1 and 2, phase-portraits
-Internal stability: Lyapunov and asymptotic stability and their verifications by using Lyapunov functions
- External stability: comparison functions and their use in the study of Input-to-State stability and related notions
- Stability of interconnected systems: series, paralle and feedback; small gain theorem
- Contraction theory
-Dissipative and passive systems
- Monotone systems and implications of monotonicity in the qualitative study of their dynamical behaviours
-Nonlinear dynamical system in dimension 1 and 2, phase-portraits
-Internal stability: Lyapunov and asymptotic stability and their verifications by using Lyapunov functions
- External stability: comparison functions and their use in the study of Input-to-State stability and related notions
- Stability of interconnected systems: series, paralle and feedback; small gain theorem
- Contraction theory
-Dissipative and passive systems
- Monotone systems and implications of monotonicity in the qualitative study of their dynamical behaviours