25794: Nonlinear Systems
Course Name: Nonlinear Systems
Course Number: 25794
Prerequisite(s): 25411 (Linear Control Systems) or 25752 (Linear Control Systems and Lab)
Co-requisite(s): -
Units: 3
Level: Undergraduate
Last Revision: Spring 2015
Description:
Syllabus:
References:
Course Number: 25794
Prerequisite(s): 25411 (Linear Control Systems) or 25752 (Linear Control Systems and Lab)
Co-requisite(s): -
Units: 3
Level: Undergraduate
Last Revision: Spring 2015
Description:
The objectives of this course are as follows:
- Expanding students’ knowledge and understanding of nonlinear phenomena and their associated effects
- Familiarizing students with the theory of dynamical systems
- Integrating abstract theoretical concepts with tangible control-related ideas
Syllabus:
- Introduction to the theory of dynamical systems, mappings, and functions
- Review of linear systems
- Nonlinear systems and the possible phenomena within them
- Linearization and its conditions
- Phase plane analysis for second-order systems
- Lyapunov stability theory
- Periodic orbits: Poincaré and Bendixson theorems
- Averaging method and Poincaré map for analyzing periodic orbits
- Bifurcation theory
- Utilizing feedback for controlling nonlinear systems
- Basic concepts related to chaos
References:
- L. Perko, Differential Equations and Dynamical Systems, Springer-Verlag
- S. H. Strogatz, Nonlinear Dynamics and chaos, 1994
- J. J. Slotine, W. Li, Applied Nonlinear Control, Prentice Hall, 1991
- J. Gwckenheimer and P. Holmes, Nonlinear Oscillations, Dynamical systems and Bifurcations of Vectors Fields, Springer-Verlag, 1983
Last Update: 2024-06-11