Behavioural Theory of Systems with a View Toward Data Driven Control

By Prof. Debasattam Pal | IIT Bombay

Learners enrolled: 189 | Exam registration: 2

ABOUT THE COURSE:

Data-driven control is the emerging new tool for designing control systems without explicitly constructing the model either from experiments or from first principles. The behavioural approach to systems theory is particularly suited for data-driven control because it puts the “behaviour” of the system, i.e., the set of trajectories that a system admits, at the centre-stage and not its model. In this course we shall first learn the basics of behavioural theory. We shall then use these ideas to explore the data-driven methodologies of control. In the process we shall understand the fundamental idea behind data-driven control, namely, the notion of persistency of excitation.

INTENDED AUDIENCE: Anyone with a BE/BTech having done a UG level course on control theory, or with an MSc in mathematics having done courses on dynamical systems can go through this course.

PREREQUISITES: Basic course on control theory, preliminary linear algebra.

INDUSTRY SUPPORT: Any company that does control systems design: aerospace, robotics, chemical processes, etc. should value/recognize this online course. For example, Eaton, Honeywell, GE, ABB, etc.

Summary

Course Status :	Upcoming
Course Type :	Elective
Language for course content :	English
Duration :	8 weeks
Category :	Electrical, Electronics and Communications Engineering Control and Instrumentation
Credit Points :	2
Level :	Postgraduate
Start Date :	17 Feb 2025
End Date :	11 Apr 2025
Enrollment Ends :	17 Feb 2025
Exam Registration Ends :	24 Feb 2025
Exam Date :	27 Apr 2025 IST

Note: This exam date is subject to change based on seat availability. You can check final exam date on your hall ticket.

Page Visits

Course layout

Week 1: Introduction: Systems, behaviours, dynamical systems. Fundamental properties: linearity,shift/time-invariance.

Week 2: Models and representations: AR, MA, ARMA. Kernel, image, latent variables.

Week 3: Behaviours and modules: The fundamental principle and elimination theory.

Week 4: Two crucial concepts: Controllability and observability.

Week 5: From time series to linear systems: the most powerful unfalsified model.

Week 6: The fundamental lemma of data-driven approach: persistency of excitation.

Week 7: Data-driven control: Data-driven satbilization.

Week 8: Data-drive control (contd.): Data informativity.

Books and references

[1] J. W. Polderman and J. C. Willems, Systems Theory: a Behavioral Approach, Springer, 1998.

[2] J. C. Willems, P. Rapisarda, I. Markovsky and B. L. De Moor, “A note on persistency of excitation,” Systems and Control Letters, 54:4, pp. 325–329, 2005.

[3] C. de Persis and P. Tesi, “Formulas for Data-Driven Control: Stabilization, Optimality, and Robustness” IEEE Transactions on Automatic Control, 65:3, pp 909-924, 2020.

[4] H. J. van Waarde , J. Eising , H. L. Trentelman and M. K. Camlibel, “Data Informativity: A New Perspective on Data-Driven Analysis and Control”, IEEE Transactions on Automatic Control, 65:11, pp 4753-4768, 2020.

Instructor bio

Prof. Debasattam Pal

IIT Bombay

Prof.Debasattam Pal is an Associate professor at the Department of Electrical Engineering, IIT Bombay. He did his MTech and PhD from IIT Bombay in the years 2007 and 2012, respectively. He has published over 70 original research articles in themost reputed journals and onferences. His areas of interest include algebraic-geometric analysis of systems, dissipativity theory, switched systems, optimal control and multi-agent systems.

Course certificate

The course is free to enroll and learn from. But if you want a certificate, you have to register and write the proctored exam conducted by us in person at any of the designated exam centres.

The exam is optional for a fee of Rs 1000/- (Rupees one thousand only).

Date and Time of Exams:April 27, 2025 Morning session 9am to 12 noon; Afternoon Session 2pm to 5pm.

Registration url: Announcements will be made when the registration form is open for registrations.

The online registration form has to be filled and the certification exam fee needs to be paid. More details will be made available when the exam registration form is published. If there are any changes, it will be mentioned then.

Please check the form for more details on the cities where the exams will be held, the conditions you agree to when you fill the form etc.

CRITERIA TO GET A CERTIFICATE

Average assignment score = 25% of average of best 6 assignments out of the total 8 assignments given in the course.
Exam score = 75% of the proctored certification exam score out of 100

Final score = Average assignment score + Exam score

Please note that assignments encompass all types (including quizzes, programming tasks, and essay submissions) available in the specific week.

YOU WILL BE ELIGIBLE FOR A CERTIFICATE ONLY IF AVERAGE ASSIGNMENT SCORE >=10/25 AND EXAM SCORE >= 30/75. If one of the 2 criteria is not met, you will not get the certificate even if the Final score >= 40/100.

Certificate will have your name, photograph and the score in the final exam with the breakup.It will have the logos of NPTEL and IIT Bombay .It will be e-verifiable at nptel.ac.in/noc.

Only the e-certificate will be made available. Hard copies will not be dispatched.

Once again, thanks for your interest in our online courses and certification. Happy learning.

- NPTEL team