NPTEL - Dynamical Systems and Control
offered by IIT Roorkee

Public/Government Institute
Estd. 1847

Dynamical Systems and Control
at
IIT Roorkee
Overview

Enhance the understanding of the theory, properties and applications of various dynamical and control systems

Duration	12 weeks
Mode of learning	Online
Credential	Certificate

Dynamical Systems and Control
at
IIT Roorkee
Highlights

Earn a E- certificate of completion from IIT Roorkee

Dynamical Systems and Control
at
IIT Roorkee
Course details

Who should do this course?

For UG/PG students of technical institutions/ universities/colleges

More about this course

The participants will also be conversant with the controllability, stabilizability and optimal control aspects of a dynamical system
Most Dynamical systems-physical, social, biological, engineering are often conveniently expressed (modeled) in the form of differential equations with or without control
In this context this course has tremendous applications in diverse fields of engineering and technology
After completing the course one may be able to understand some of the important aspects of dynamical systems such as mathematical modeling, well posedness (existence, uniqueness and stability) of the considered problem

Dynamical Systems and Control
at
IIT Roorkee
Curriculum

Week 1

Formulation of physical systems-I

Formulation of physical systems-II

Existence and uniqueness theorems-I

Existence and uniqueness theorems-II

Linear systems-I

Week 2

Linear Systems-II

Solution of linear systems-I

Solution of linear systems?II

Solution of linear systems-III

Fundamental Matrix-I

Week 3

Fundamental Matrix-II

Fundamental matrices for non- autonomous systems

Solution of non-homogeneous systems

Stability of systems

Equilibrium points

Stability of linear autonomous systems-I

Week 4

Stability of linear autonomous systems-II

Stability of linear autonomous systems-III

Stability of weakly non- linear systems-I

Stability of weakly non- linear systems-II

Stability of non- linear systems using linearization

Week 5

Properties of phase portrait

Properties of orbits

Phase portrait

Types of critical points

Phase portrait of linear differential equations-I

Phase portrait of linear differential equations-II

Week 6

Phase portrait of linear differential equations-III

Poincare Bendixson Theorem

Limit cycle

Lyapunov stability-I

Lyapunov stability?II

Week 7

Introduction to Control Systems-I

Introduction to Control Systems-II

Controllability of Autonomous Systems

Controllability of Non-autonomous Systems

Observability-I

Week 8

Observability-II

Results on Controllability and Observability

Companion Form

Feedback Control-I

Feedback Control-II

Week 9

Feedback Control-III

Feedback Control-IV

State Observer

Stabilizability

Introduction to Discrete Systems-I

Week 10

Introduction to Discrete Systems-II

Lyapunov Stability Theory-I

Lyapunov Stability Theory-II

Lyapunov Stability Theory-III

Optimal Control- I

Week 11

Optimal Control-II

Optimal Control-III

Optimal Control- IV

Optimal Control for Discrete Systems-I

Optimal Control for Discrete Systems-II

Week 12

Controllability of Discrete Systems

Observability of Discrete Systems

Stability for Discrete Systems

Relation between Continuous and Discrete Systems-I

Relation between Continuous and Discrete Systems-II

Dynamical Systems and Control
at
IIT Roorkee
Faculty details

Prof. D. N. Pandey

Dr. D. N. Pandey is an Associate Professor in the Department of Mathematics, IIT Roorkee. Before joining IIT Roorkee, he worked as a faculty member in BITS-Pilani Goa campus and LNMIIT Jaipur. His area of expertise includes semigroup theory and functional differential equations of fractional and integral orders.

Dr. N. Sukavanam

He is a Professor in the Department of Mathematics, IIT Roorkee. His area of research includes Control Theory and Robotics. He has supervised nineteen Ph.D. thesis and has published more than 80 research papers in reputed international journals.