Course10810571859 lectures
Convex Optimization in Control
Prof. Ashish Ranjan Hota · IIT Kharagpur
About
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.
Lectures
Week 1
- Lecture 01 : Introduction
- Lecture 02 : Optimal Solution and Optimality Conditions
- Lecture 03 : Convex Sets
- Lecture 04 : Convex Functions
- Lecture 05 : Convex Functions (Contd.)
Week 2
- Lecture 06 : Convex Optimization
- Lecture 07 : Linear Programming
- Lecture 08 : Linear Programming Duality
- Lecture 09 : LP and Lagrangian Duality
- Lecture 10 : Lagrangian Duality
Week 3
- Lecture 11 : Programming Demonstration
- Lecture 12 : : Programming Demonstration(Contd.)
- Lecture 13 : Linear Matrix Inequalities
- Lecture 14 : Linear Matrix Inequalities (Contd.)
- Lecture 15 : Linear Matrix Inequalities
Week 4
- Lecture 16 : Dynamical Systems and Lyapunov Stability
- Lecture 17 : Continuous-time LTI System
- Lecture 18 : Lyapunov Stability and LMIs
- Lecture 19 : D-Stability
Week 5
- Lecture 21 : Controllability
- Lecture 22 : State Feedback Control
- Lecture 23 : Luenberger Observers
- Lecture 24 : Analysis for Discrete-time Systems
- Lecture 25 : Programming Demo.
Week 6
- Lecture 26 : Programming Demo.
- Lecture 27 Signal Norms
- Lecture 28 : H_2 and H_Inf Spaces
- Lecture 29 : LMIs for H_Inf Norm
- Lecture 30 : H_Inf Optimal State Feedback Control
Week 7
- Lecture 31 : Programming Demo.
- Lecture 32 : H_2 Norm and LMIs
- Lecture 33 : H_2 State Feedback Control and LQR
- Lecture 34 : H_2 and H_Infinity Optimal Observer Design
- Lecture 35 : Programming Demo.
Week 8
- Lecture 36 : Optimal Control Framework
- Lecture 37 : Well-Posedness and Stability
- Lecture 38 : Optimal Dynamic Output Feedback Control
- Lecture 39 : Optimal Dynamic Output Feedback Control Cont.
- Lecture 40 : Programming Demo
Week 9
- Lecture 41 : H-Infinity Norm for Discrete-Time LTI Systems
- Lecture 42 : H-2 Norm for Discrete-Time LTI Systems
- Lecture 43 : Stability Notions for Uncertain Systems
- Lecture 44 : Quadratic Stability and State-Feedback Synthesis
- Lecture 45 : Programming Demo.
Week 10
- Lecture 46 : Dissipative Dynamical Systems
- Lecture 47 : Dissipative LTI Systems and LMIs
- Lecture 48 : Representing Uncertain Systems
- Lecture 49 : Integral Quadratic Constraints
- Lecture 50 : LMI for Robust L2 gain via IQC
Week 11
- Lecture 51 : IQCs for Discrete-Time Systems
- Lecture 52 : Parametric Norm-Bounded Uncertainty
- Lecture 53 : Programming Demo
- Lecture 54 : Gradient -based Algorithms
- Lecture 55 : Convergence of Gradient Descent
Week 12
Syllabus and materials
At NPTEL, as the course publishes them.
Credits and licence
- Institution
- IIT Kharagpur
- Department
- Electrical Engineering
- Teacher
- Prof. Ashish Ranjan Hota
- Level
- Graduate
- Language
- English
- Subjects
- Engineering
- Source
- NPTEL
- Licence
- CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
- Attribution
- NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
- Who can watch
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