Convex Optimization in Control

By Prof. Ashish Ranjan Hota | IIT Kharagpur

Learners enrolled: 310 | Exam registration: 13

ABOUT THE COURSE:

Applications of convex optimization techniques, particularly semidefinite programming and linear matrix inequalities (LMIs), have significantly enriched the theory of optimal and robust control in the past few decades. In this course, first the theory of duality in convex programming and semidefinite programming will be covered. Then, problems pertaining to stability analysis, optimal state feedback controller synthesis, robust stability analysis and robust controller synthesis of linear dynamical systems will be studied and reformulated in terms of LMIs. The underlying theory of dissipativity and integral quadratic constraints will also be covered. Finally, applications of the above tools in the analysis and synthesis of convex optimization algorithms will be discussed. The mathematical treatment will be complemented with an extensive programming and implementation component.

INTENDED AUDIENCE: M.Tech and PhD Students in Control Systems specialization as well faculty members from different colleges. The course will also be accessible to final year UG students.

PREREQUISITES: The learners should have attended a course on linear systems/control theory from a state-space point of view. Attending an introductory course on optimization would also be helpful.

INDUSTRY SUPPORT: Mathworks, General Electric, ABB, DRDO, ISRO, Tata Motors, Adani Defence and Aerospace

Summary

Course Status :	Ongoing
Course Type :	Core
Language for course content :	English
Duration :	12 weeks
Category :	Electrical, Electronics and Communications Engineering Control and Instrumentation
Credit Points :	3
Level :	Postgraduate
Start Date :	21 Jul 2025
End Date :	10 Oct 2025
Enrollment Ends :	04 Aug 2025
Exam Registration Ends :	18 Aug 2025
Exam Date :	01 Nov 2025 IST
NCrF Level	4.5 — 8.0

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 to Convex Optimization: Convex Sets, Convex Functions

Week 2: Duality: Farka’s Lemma, Strong Duality in Linear Programming, Lagrangian duality, KKT Optimality Conditions

Week 3: Linear Matrix Inequalities (LMIs), Semidefinite Programming (SDP), SDP duality, Schur Complement Lemma, Examples

Week 4: Linear Dynamical Systems in State-Space Form, Lyapunov Stability, LMI Conditions for Stability of Continuous and Discrete-time Systems

Week 5: LMI Conditions for Controllability and State Feedback, Observability and Observer Design

Week 6: Signal Spaces, Operators, Norms for Systems and Transfer Functions

Week 7: Stabilizing Controllers and LMI Characterizations, H_2 and H_Infinity Optimal Control and State Feedback Synthesis via LMIs

Week 8: H_2 and H_Infinity optimal observer synthesis, Optimal Control Framework, LMIs for H_Infinity Output Feedback Synthesis

Week 9: H_2 and H_Infinity norms for Discrete-time LTI Systems, Uncertain Systems, Quadratic Stability with Affine, Polytopic and Interval Uncertainty

Week 10: General representation of uncertain systems, Dissipativity, Quadratic and Integral Quadratic Constraints (IQC) and their LMI Characterizations

Week 11: Robust Stability Analysis and Controller Design for structured uncertainty and via IQC

Week 12: Analysis of Optimization Algorithms as Robust Control Problems: Dissipativity and IQC based approaches

Books and references

Duan, G.R. and Yu, H.H., 2013. LMIs in control systems: analysis, design and applications. CRC press.
Calafiore, Giuseppe C., and Laurent El Ghaoui. Optimization models. Cambridge university press, 2014.
Dullerud, G.E. and Paganini, F., 2013. A course in robust control theory: A convex approach (Vol. 36). Springer Science & Business Media.
Scherer, C. and Weiland, S., 2000. Linear matrix inequalities in control. Lecture Notes, Dutch Institute for Systems and Control, Delft, The Netherlands, 3(2).
Lessard, L., 2022. The analysis of optimization algorithms: A dissipativity approach. IEEE Control Systems Magazine, 42(3), pp.58-72.
Scherer, C.W., Ebenbauer, C. and Holicki, T., 2023, December. Optimization algorithm synthesis based on integral quadratic constraints: A tutorial. In 2023 62nd IEEE Conference on Decision and Control (CDC) (pp. 2995-3002). IEEE.
Fatma Kılın¸c-Karzan and Arkadi Nemirovski, Essential Mathematics for Convex Optimization. Lecture Notes. Available online at https://www2.isye.gatech.edu/~nemirovs/KKN.pdf

Instructor bio

Prof. Ashish Ranjan Hota

IIT Kharagpur

Prof. Ashish R. Hota received the B.Tech. and M.Tech. degrees (dual degree) from the Indian Institute of Technology (IIT) Kharagpur, Kharagpur, India, in 2012, and the Ph.D. from Purdue University, West Lafayette, IN, USA, in 2017, all in Electrical Engineering. He was a Postdoctoral Researcher with the Automatic Control Laboratory, ETH Zurich in 2018. He has been an Assistant Professor with the Department of Electrical Engineering, IIT Kharagpur since January 2019. He was recognized as a Young Associate of the Indian National Academy of Engineering (INAE) in 2023, received the Outstanding Graduate Researcher Award from the College of Engineering, Purdue University in 2017, and the Institute Silver Medal from IIT Kharagpur in 2012. His research interests are in the areas of stochastic optimization, optimization-based control, game theory and control of network 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: November 01, 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 8 assignments out of the total 12 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 Kharagpur. 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

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