## Advanced Topics in Systems & Control (ELL808)## Time and Venue (Semester-I, 2024-25)Tuesday: 3:30 PM - 5 PM (LH 622) Friday: 3:30 PM - 5 PM (LH 622)
## Course DescriptionThe Advanced Topics in Systems & Control is a graduate-level course. In this course, it is planned to cover various optimization techniques that are required for control system analysis and design ( ). The major contents of this course are: convex analysis and optimization, duality theory, LMI (linear matrix inequality) optimization and distributed optimization.*Optimizations for Control*
## Syllabus (Tentative)**Mathematical Preliminaries**
**Convex Analysis**Convex set and its topological properties, Afffine subspace and affine hull, Convex hull, Cones, Convex and concave functions, Caratheodory theorem, Helley theorem (LN 5, LN 6, LN 7, LN 8). *Polyhedral convexity theory*: Hyperplanes, Halfspaces, Polyhedral set, Simplex, Cones, Separating Hyperplane, Supporting Hyperplane, Polar and Dual cones, Polyhedral cones, Farkas Lemma, Extreme Points.
**Convex Optimization**Unconstrained and Constrained optimizations, Local and global optima, Optimality conditions, Linear Programming (LP), Quadratic Programming (QP), Conic Programming (CP), Semidefinite Programming (SDP/LMI optimizations).
**Duality Theory**Lagrange multipliers, Optimality conditions, KKT condition, Complementary slackness, Lagrangian dual function, Weak and Strong duality, Slater's constraint qualification, Dual optimization formulation.
**Algorithms for Optimization**Descent methods, Newton's method, Interior-point methods
**Introduction to Distributed Optimization**
## Lecture NotesWill be provided.
## EvaluationHomework/Assignment: 30 % Mid-sem Exam: 30% End-sem Exam: 40%
## Suggested References*Convex Analysis & Optimization*by D. P. Bertsekas, A. Nedic and A. E. Ozdaglar*Nonlinear Programming*by D. P. Bertsekas,*Convex Optimization*by S. Boyd and L. Vandenberghe*Lectures on Modern Convex Optimization*by Aharon BenTal and Arkadi Nemirovski.
## Relevant materials |