Control Theory for Differential Equations (2022)

Convener(s)

 
Name: Dr. Shirshendu Chowdhury Dr. Rajib Dutta
Mailing Address: Indian Institute of Science and Research - Kolkata, Mohanpur, Nadia – 741246,
West Bengal, India		 Indian Institute of Science and Research - Kolkata, Mohanpur, Nadia – 741246,
West Bengal, India
Email: shirshendu at iiserkol.ac.in rajib.dutta at iiserkol.ac.in

This NCMW aims to introduce the participants to the control theory for systems governed by ordinary differential equations (ODE) . The motivation comes from the need to understand and control the differential equations modeling various physical phenomena. The controllability problem, generally speaking, is to move a dynamical system by means of suitable control (input), from one state to the desired state in finite time, whereas stabilizability refers to the system being brought to rest or an equilibrium state as time tends to infinity.In the first week we plan to discuss some topics from existence and stability for linear and nonlinear ODE, that are required for the subsequent lectures. In the second week, we introduce the notion of controllability and stabilizability for the finite dimensional linear systems and establish several criteria and techniques to check controllability or stabilizability of a system. At the end of second week, we will focus on controllability and stabilizability of some nonlinear differential equations using various new methods, like Iterated Lie brackets technique and phantom tracking method (as explained in the book and recent papers of Jean Michel Coron). These methods have wide ranging applicationsin current research on control of Partial Differential Equations, to be covered in a later workshop.

 

 

Dates: 

Monday, November 28, 2022 - 11:15 to Saturday, December 10, 2022 - 11:15

Venue: 

Venue Address: 

IISER Kolkata, Dept. Of Mathematics and Statistics, Mohanpur, Nadia, West Bengal-741246

Venue State: 

Venue City: 

PIN: 

741246

Chrono Order: 

402

Syllabus: 

 Name of the possible Speakers with affiliations

  1. Dr Saugata Bandyopadhyay, IISER Kolkata
  2. Dr Rajib Dutta, IISER Kolkata
  3. Dr. Shirshendu Chowdhury, IISER Kolkata
  4. Prof. Mythily Ramaswamy , ICTS-TIFR, Bangalore
  5. Dr. Debanjana Mitra, IIT Bombay.
  6. Dr. Debayan Maity , TIFR-CAM, Bangalore

Possible Tutorial Assistants :

S. No.

Name

Affiliation

1

Samprita Das Roy

IISER Kolkata

2

Subrata Mazumdar

IISER Kolkata

3

Jiten Kumbhakar

IISER Kolkata

4

Wasim Akram

IIT Bombay

5

Sakil Ahamed

IIT Bombay

6

Manish Kumar

IISER Kolkata

 

Syllabus:

First week: (Existence and Stability of ODE in R^N)

  1. Existence and stability for Linear ODE:Linear ODE, Exponential of Matrix, Global existence Theorem for linear ODE,(from [7], [8] )Linear stability (eigenvalue criteria from [9]),
  2. Existence and stability for Non-Linear ODE:Nonlinear ODE, Picard iteration, existence uniqueness theorem ([7] , [8]), stability of nonlinear ODE, Lyapunov’s Method([7]), LaSalle's invariance principle([4]

    Second week: (Controllability and Stabilizability in R^N for linear and nonlinear ODE)

  3.  Controllability and Stabilizability for Linear ODE:Finite dimensional linear system, Various concepts of controllability. Reachable states. Kalman rank condition, Popov-Belevitch-Hautus test. The moment method and HUM control. Concepts of observability, duality between controllability and observability, cost of the control. ( [1],[2],[5],[6],[9]). Stabilizability for linear system, Popov-Belevitch-Hautus test, Feedback stabilization, pole shifting, Gramian, Complete stabilization, relation between null controllability and stabilizability ([2], [5], [9]).
  4. Controllability and Stabilizability for Non- Linear ODE:Controllability for nonlinear systems in finite dimension: Fixed point method, Return method,Quasi-static deformation method and Power series expansion method, Iterated Lie bracket stechnique (Lie algebra Rank condition) from [2] and phantom tracking method (from [3] as application of Lyapunov method and Lasalle's invariance principle).

 

References:

  1. Franck Boyer. Controllability of linear parabolic equations and systems, 2020. Lecture Notes, https://hal.archives-ouvertes.fr/hal-02470625.
  2. Jean-Michel Coron, Control and nonlinearity. Mathematical Surveys and Monographs, 136. American Mathematical Society, Providence, RI, 2007.
  3. Jean-Michel Coron, Phantom Tracking method, homogeneity and rapid stabilization. Math. Control Relat. Fields3(2013), no. 3,303-322.
  4. Jean-Michel Coron, Ivonne Rivas, Quadratic approximation and time-varying feedback laws. SIAM J. Control Optim.55 (2017), no. 6, 3726-3749.
  5. Hassan K. Khalil, Nonlinear systems. Macmillan Publishing Company, New York, 1992
  6. Weijiu Liu, Elementary Feedback Stabilization of the Linear Reaction-Convection-Diffusion Equation and the Wave Equation, Mathématiques & Applications (Berlin) [Mathematics & Applications], 66. Springer-Verlag, Berlin, 2010.
  7. Sorin Micu and Enrique Zuazua, An Introduction to the Controllability of Partial Differential Equations. Available at http://www.uam.es/personal_pdi/ciencias/ezuazua/informweb/argel.pdf.
  8. Lawrence Perko, Differential Equations and Dynamical Systems.Third edition. Texts in Applied Mathematics, 7.
  9. Springer-Verlag, New York, 2001.9. George Simmons, Differential Equations with Applications and Historical Notes. Third edition, Textbooks in Mathematics. CRC Press, Boca Raton, FL, 2017
  10. Jerzy Zabczyk, Mathematical control theory. An introduction. Modern Birkhäuser Classics. , Inc., Boton, MA, 1995.

 

Time Table: 

 

Date

Lecture 1

(9.30–11.00)

Tea

(11.00 –11.30)

Lecture 2

(11.30–1.00)

Lunch

(1.00–2.00)

Lecture 3

(2–3.30)

Tea

(3.30-4.00)

Tutorial/

Discussion

(4.00-5.30)

Snacks

5.30

1st week

 

 

 

 

T

 

 

E

 

 

A

 

 

 

 

L

 

U

 

N

 

C

 

H

 

 

 

T

 

 

E

 

 

A

(Speaker + two tutors)

 

 

 

S

 

N

 

A

 

C

 

K

 

S

28/11/2022

 

Saugata

Rajib

Shirshendu

Sagata+

Samprita+Subrata

29/11/2022

Saugata

Rajib

Shirshendu

Rajib+

Jiten+Wasim

30/11/2022

Saugata

Rajib

Shirshendu

Shirshendu

+Sakil+Manish

01/12/2022

Saugata

Rajib

Shirshendu

Saugata+

Samprita+Subrata

02/12/2022

Saugata

Rajib

Shirshendu

Rajib+ Jiten+Wasim

03/13/2022

Saugata

Rajib

Shirshendu

Shirshendu

+Sakil+Manish

2nd week

 

 

 

 

 

 

 

 

05/13/2022

Mythily

 

 

T

 

 

E

 

 

A

Debanjana

 

 

L

 

U

 

N

 

C

 

H

Debayan

 

 

T

 

 

E

 

 

A

Mythily+

Samprita+Subrata

 

S

 

N

 

A

 

C

 

K

 

S

06/12/2022

Mythily

Debanjana

Debayan

Debanjana+

+Jiten+Wasim

07/12/2022

Mythily

Debanjana

Debayan

Debayan+

+Sakil+Manish

08/12/2022

Mythily

Debanjana

Debayan

Mythily+

Samprita+Subrata

09/12/2022

Mythily

Debanjana

Debayan

Debanjana+

+Jiten+Wasim

10/12/2022

Mythily

Debanjana

Debayan

Debayan+

+Sakil+Manish

 

 

Selected Applicants: 

 NOTE: Selected outstation applicants should confirm their participation through email to shirshendu@iiserkol.ac.inby 23rd October 2022. If a selected outstation  candidate  fails to confirm his/her participation by 23rd October, 2022  then wait listed candidates will be given the opportunity and they will be informed through email.

 

Sr. SID Full Name Affiliation Gender Position in College / Univ Univ / Inst M.Sc./ M.A. Year of Passing M.Sc./ M.A Ph.D.
Deg.
Selected Outstation Participants          
1 41398 Mr. Arindam Basak IIT Kharagpur Male PhD IIT Patna 2020  
2 41763 Ms Manika Bag IISER TVM Female Int. PhD IISER TVM 2022  
3 41772 Ms Greeshma K IISER TVM Female PhD Cental University of Kerala 2020  
4 41852 Mr Sagar Gautam IIT Roorkee Male PhD University of Lucknow 2019  
5 42558 Mr. Rohit Kumar Indian Institute of Technology Jodhpur Male PhD University of Lucknow 2018  
6 42564 Mr. Ritabrata Jana IISER TVM Male PhD Banaras Hindu University 2019  
7 42688 Mr. Anubrata Singharoy IIT Roorkee Male Phd Ramakrishna Mission Vivekananda University 2021  
8 42694 Mr Md Arzoo Jamal Indian Institute of Technology (BHU), Varanasi Male PhD Jamia Millia Islamia 2016  
9 42697 Mr. Inzamamul Haque DEPARTMENT OF MATHEMATICS, ALIGARH MUSLIM UNIVERSITY ALIGARH Male PhD Aligarh Muslim University , Aligarh 2017  
10 42759 Ms Shivasiva Priyaa R S Periyar University Female Ph.D Research Scholar M.Sc 2018  
11 42789 Mr. Lovelesh Sharma INDIAN INSTITUTE OF TECHNOLOGY JODHPUR Male PhD Central University of South Bihar, Patna 2018  
12 42858 Mr. Sunil Sunil IIT Guwahati Male PhD Student Jaipur National University, Jaipur. 2017  
13 42883 Mr Ajith Kumar T Niser Bhubaneswar Male Ph D student University of Madras 2019  
14 42920 Mr. Ragul Ravi Bharathiar University Male PhD Ramakrishna mission vidyalaya college of arts and science, Coimbatore 2017  
15 42949 Mr Muthuraj T Indira Gandhi Centre for Atomic Research Male PhD Bharathiar university 2018  
16 42957 Mr. Rahul Barthwal IIT Kharagpur Male PhD M.Sc. 2017  
17 42975 Ms. Stuti Das IIT Kanpur Female PhD Jadavpur University 2021  
18 42987 Mr. Vivek Sahu IIT Kanpur Male Research Scholar IIT Guwahati 2020  
19 43021 Mr. Mohmedmunavvar Mubarak Bapu IIT Kanpur Male PhD Sardar Patel University, VVN 2018  
20 43027 Mr. Vellappandi M National Institute of Technology Puducherry Male Ph.D. Bharathiar University 2017  
21 43063 Ms Jyotsna Kumari Bharti NATIONAL INSTITUTE OF TECHNOLOGY TRICHY Female Phd C.V RAMAN COLLEGE OF ENNGINEERING BHUBHANEWAR 2018  
22 43065 Mr. Sumit Maity NIT Andhra Pradesh Male PhD student Vidyasagar University 2019  
23 43075 Mr. Vishal Neeraje International Centre for Theoretical Sciences -TIFR Male PhD Indian Statistical Institute 2021  
24 43086 Mr. Pardeep Kumar Indian Institute of Technology Roorkee Male Research Scholar South Asian University, New Delhi 2015  
25 43105 Ms. Ambalika Halder NIT Andhra Pradesh Female PhD JADAVPUR UNIVERSITY 2019  
26 43158 Mr. Arghya Kundu IIT Kharagpur Male PhD Research Scholar Ballygunge Science College (Calcutta University) 2018  
27 43184 Dr Ashis Kumar Pati CV Raman Global University Male Asst Prof IISER Kolkata 2014 02/06/2022
28 43194 Mr. Bholanath Kumbhakar INDIAN INSTITUTE OF TECHNOLOGY ROORKEE Male Ph. D. THE UNIVERSITY OF BURDWAN 2018  
29 43249 Ms. Sagarika Dutta UNIVERSITY OF CALCUTTA Female MSc STUDENT UNIVERSITY OF CALCUTTA 2022  
30 43342 Ms Anuvertika Pandey National Institute of Science Education and Research Female PhD student Banaras Hindu University 2020  
Local Participants          
1 41303 Dr Avijit Sarkar University of Kalyani Male Teacher University of Kalyani 2002  
2 42870 Mr. Debanjit Mondal IISER KOLKATA Male Integrated PhD Student IISER KOLKATA 2022  
3 42884 Mr. Niren Biswas University of Calcutta Male PhD University of Calcutta 2019  
4 42917 Mr. Tshering Dorjee Bhutia RAMAKRISHNA MISSION RESIDENTIAL COLLEGE (Autonomous) Male Asst Prof IIT DELHI 2017  
5 43039 Mr. Kalyanashis Sahoo University of Calcutta Male PhD Vidyasagar University 2014  
6 43238 Mr. Rakesh Medda University of Kalyani Male PhD Research Scholar University of Kalyani 2016  
7 43244 Ms. Srijita Mondal Jadavpur University Female PhD Student IIT Kharagpur 2016  
Wait-listed Participants          
1 43010 Mr. Vishnukumar K S National Institute of Technology Puducherry Male PhD Thiagarajar College 2021  
2 43277 Mr. Rishabh Sharma Indian Institute of Technology, Patna Male PhD Indian Institute of Technology, Patna 2018  
3 41936 Ms. Nanditha C K IISER TVM Female PhD Student IISER TVM 2018  
4 42895 Mr. Bhanu Prakash D Sri Sathya Sai Institute of Higher Learning Male PhD Student Sri Sathya Sai Institute of Higher Learning 2020  
5 41405 Mr. Shiba Biswas Indian Institute of Technology Kharagpur Male Ph.D. Scholar University of North Bengal 2019  
6 42875 Mr Arnab Mapui Indian Institute of Technology (BHU) Varanasi Male PhD Visva-Bharati University 2019  
7 42566 Ms Saranya G THE GANDHIGRAM RURAL INSTITUTE (DEEMED TO BE UNIVERSITY) Female Ph.D. THE GANDHIGRAM RURAL INSTITUTE (DEEMED TO BE UNIVERSITY) 2021  
8 42239 Ms. Sarbani Pramanik IISER TVM Female IPhD IISER TVM Appeared / Awaiting Result  
9 41962 Mr. Saroj Si IIT Roorkee Male PhD Utkal University, Vanivihar 2018  
10 42909 Mr Abhinav Kumar National Institute of Technology Jamshedpur Male Research Scholar Central University of South Bihar 2018  
11 43055 Ms Ilavarasi R ERODE ARTS AND SCIENCE COLLEGE (Autonomous) Female Ph.D., M.Sc. 2017  
12 43062 Mr. Arunkumar M National Institute of Technology, Tiruchirappalli. Male PhD Scholar PSG College of Arts and Science 2021  
13 43103 Mr. Sarabindu Dolui National Institute of Technology, Andhra Pradesh Male Ph.D. B.H.U. 2018  
14 42579 Ms Varshini Sandrasekaran PSG COLLEGE OF ARTS & SCIENCE Female PhD Research Scholar PSG COLLEGE OF ARTS & SCIENCE 2018  
15 42202 Ms. Shanmuga Priya R S PSGR Krishnammal College For Women Female phD student Bharathiar University 2018  
16 42616 Ms. Priyanka M THE GANDHIGRAM RURAL INSTITUTE (DEEMED TO BE UNIVERSITY) Female Ph.D. THE GANDHIGRAM RURAL INSTITUTE (DEEMED TO BE UNIVERSITY) 2020  
17 42912 Mr. Aniruddha Seal Indian Institute of Technology Guwahati Male PhD Indian Institute of Engineering Science and Technology, Shibpur, M.Sc. 2017  
18 42634 Mr. Sandip Maji Indian Institute of Technology Guwahati. Male PhD IIT Madras 2018  
19 43157 Mr. Ayush Agrawal IIT Roorkee Male PhD IIT Gandhinagar 2019  
20 42919 Ms. Garima Gupta Indian Institute of Technology, Roorkee Female PhD Indian Institute of Technology Bhubaneshwar 2017  

How to Reach: 

Click here

School Short Name: 

ctde

Last Date Application: 

Friday, November 5, 2021

School Type: 

NCMW

Separate faculty form: 

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