E1 242: Nonlinear
systems and control (3:0)
Announcements
- First class: Tuesday, 7 Jan
- If you are interested in the course, then please enrol for it on moodle.
Time and venue
Class timings: Tuesdays, Thursdays 15:30-17:00
Venue: EE B 303
Instructor
Pavan Tallapragada
Office: EE C-323
email: pavant@iisc.ac.in
(prefix “NSC”, without quotes, in email subject)
Course overview
This course is on the description, analysis and control of nonlinear
systems. Nonlinear systems occur everywhere - in nature and in numerous
engineering applications. So, it is very useful to a controls
practitioner or theorist to have a good understanding of nonlinear
systems and methods to design controllers for them. The focus of the
course leans towards mathematical theory and analysis. However,
interesting applications in various domains would also be discussed
frequently.
Course objectives/expected
outcomes:
- The students would learn to use various basic and commonly used
tools to analyze nonlinear systems and to design controllers for the
same.
- The students would be exposed to the complexities of nonlinear
systems as well as to applications in various domains.
Course outline
Core topics:
- Equilibria and qualitative behavior
- Existence and uniqueness of solutions
- Lyapunov stability, invariance principle, converse theorems,
ultimate boundedness, input-to-state stability
Selected topics from:
- Control Lyapunov functions and Control Barrier functions
- Contraction theory for dynamical systems
- Projected dynamical systems
- Input-output stability, small-gain theorem, passivity
- Feedback linearization, gain scheduling, sliding mode control,
backstepping
- Intro to switched and hybrid systems
- Applications in networked control such as control over channels with
quantization, sampling, time delays
- Applications in distributed systems and control such as consensus,
synchronization, coverage, etc.
- Application to Hopfield neural networks
- Applications in social systems - population dynamics and opinion
dynamics
Prerequisites
E1-241 “Dynamics of linear systems” or equivalent; Or background in
linear algebra and ordinary differential equations; Or permission of the
instructor. Familiarity with some programming language such as MATLAB or
Octave or Python is useful.
Grading
- 2 unit exams: 50%
- Homeworks and class participation: 10%
- Final exam: 40%
References
- H. K. Khalil, “Nonlinear Systems”. Prentice Hall, 3 edition,
2002.
- S. S. Sastry, “Nonlinear Systems: Analysis, Stability and Control”.
Number 10 in Interdisciplinary Applied Mathematics. Springer, 1999.
- Mathukumalli Vidyasagar, “Nonlinear systems analysis”. Society for
Industrial and Applied Mathematics, 2002.
- F. Bulo, “Contraction Theory for Dynamical Systems”. Kindle Direct
Publishing, 2024. (url)
- E. D. Sontag. “Mathematical Control Theory: Deterministic Finite
Dimensional Systems”, volume 6 of TAM. Springer, 2 edition, 1998.
Academic integrity
Please be aware of the IISc
academic integrity policy. Any violation of it will be dealt with
strictly.