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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 Description

  • The 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 (Optimizations for Control). The major contents of this course are: convex analysis and optimization, duality theory, LMI (linear matrix inequality) optimization and distributed optimization.

Syllabus (Tentative)

  • Mathematical Preliminaries

    • Linear Algebra: Vectors & matrices, Vector space and subspaces, Norms, Positive definite (semi-definite) matrices, Orthogonality, SVD (LN 1, LN 2).

    • Real Analysis: Sequences, Topological properties of sets, Functions, Continuity, Derivatives, Gradient, Hessian matrix (LN 2, LN 3, LN 4).

  • 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 Notes

  • Will be provided.

Evaluation

  • Homework/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