# E1 242: Nonlinear systems and control (3:0)

## Announcements

First class: Thursday, 5 Jan

## Time and venue

Class timings: Tuesdays, Thursdays 11:30-13:00
Venue: EE B-306

## Instructor

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

• 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.

• 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 simulation software such as MATLAB is useful.

• 2 unit exams: 50%

• Homeworks and class participation: 10%

• Final exam: 40%

## References

1. H. K. Khalil. Nonlinear Systems. Prentice Hall, 3 edition, 2002.

2. S. S. Sastry. Nonlinear Systems: Analysis, Stability and Control. Number 10 in Interdisciplinary Applied Mathematics. Springer, 1999.

3. Mathukumalli Vidyasagar. Nonlinear systems analysis. Society for Industrial and Applied Mathematics, 2002.

4. E. D. Sontag. Mathematical Control Theory: Deterministic Finite Dimensional Systems, volume 6 of TAM. Springer, 2 edition, 1998