Overview

Instructor: Prof. G. D. Ray, Department of Electrical Engineering, IIT Kharagpur.

This course deal with topics in static and dynamic optimization problems. An overview of the optimization problems, some examples of optimum design problems. Concepts and terms related to optimization problem, necessary and sufficient conditions for a multivariable function. Effects of scaling or adding a constant to an objective function and understanding of constrained and unconstrained optimization problems. Concept of Lagrange multipliers and its application to the unconstrained optimization problem. Solution of unconstrained optimization problem. Solution of constrained optimization problem using Karush-Kuhn-Tucker conditions. The basic concept of interior penalties and solution of convex optimization problem via interior point method. Linear programming. Two-phase simplex method. Primal and dual problems. Statement of Linear quadratic regulator (LQR) problem. Optimal solution of LQR problem. Frequency domain interpretation of LQR problem. Stability and robustness properties of LQR design.

Syllabus

Mod-01 Lec-01 Introduction to Optimization.
Mod-01 Lec-02 Introduction to Optimization (Contd.).
Mod-01 Lec-03 Optimality Conditions for function of several variables.
Mod-01 Lec-04 Optimality Conditions for function of several variables (Contd.).
Mod-01 Lec-05 Unconstrained optimization problem (Numerical Techniques).
Mod-01 Lec-06 Solution of unconstarined optimization problem using conjugate gradient method.
Mod-01 Lec-07 Solution of unconstarined optimization problem using conjugate gradient method.
Mod-01 Lec-08 Solution of contraint optimization problems - karush - kuhn Tucker (KKT) conditions.
Mod-01 Lec-09 Solution of contraint optimization problems - karush - kuhn Tucker (KKT).
Mod-01 Lec-10 Problem Solution Session.
Mod-01 Lec-11 Post optimality analysis, convex function and its properties.
Mod-01 Lec-12 Post optimality analysis, convex function and its properties (Contd.).
Mod-01 Lec-13 Quadratic optimization problem using Linear Programming.
Mod-01 Lec-14 Matrix form of the Simplex Method.
Mod-01 Lec-15 Matrix form of the Simplex Method (Contd.).
Mod-01 Lec-16 Solution of Linear Programming using Simplex Method - Algebraic Approach.
Mod-01 Lec-17 Solution of Linear Programming using Simplex Method - Algebraic Approach (Contd.).
Mod-01 Lec-18 Solution of LP problems with Two - Phase Method.
Mod-01 Lec-19 Solution of LP problems with Two - Phase Method (Contd.).
Mod-01 Lec-20 Standard Primal and Dual problems.
Mod-01 Lec-21 Relationship between Primal and Dual Variables.
Mod-01 Lec-22 Solution of Quadratic Programming problem using Simplex Method.
Mod-01 Lec-23 Interior point method for solving optimization problems.
Mod-01 Lec-24 Interior point method for solving optimization problems (Contd.).
Mod-01 Lec-25 Solution Non linear Programming Problem using Exterior Penalty Function Method.
Mod-01 Lec-26 Solution Non linear Programming Problem using Exterior Penalty.
Mod-01 Lec-27 Solution of Non - linear Programming Problems using interior penalty function method.
Mod-01 Lec-28 Solution of Non - linear Programming Problems using interior penalty.
Mod-01 Lec-29 Multi - variable optimization problem.
Mod-01 Lec-30 Dynamic Optimization Problem : Basic Concepts & Necessary and Sufficient Conditions.
Mod-01 Lec-31 Dynamic Optimization Problem : Basic Concepts & Necessary and Sufficient.
Mod-01 Lec-32 Dynamic Optimization Problem : Basic Concepts & Necessary.
Mod-01 Lec-33 Numerical Example and Solution of Optimal Control problem.
Mod-01 Lec-34 Numerical Example and Solution of Optimal Control problem.
Mod-01 Lec-35 Hamiltonian Formulation for Solution of optimal control problem and numerical example.
Mod-01 Lec-36 Hamiltonian Formulation for Solution of optimal control problem.
Mod-01 Lec-37 Performance Indices and Linear Quadratic Regulator Problem.
Mod-01 Lec-38 Performance Indices and Linear Quadratic Regulator Problem (Contd.).
Mod-01 Lec-39 Solution and stability analysis of finite - time LQR problem : Numerical Example.
Mod-01 Lec-40 Solution of Infinite - time LQR problem and stability analysis.
Mod-01 Lec-41 Numerical Example and Methods for Solution of A.R.E.
Mod-01 Lec-42 Numerical Example and Methods for Solution of A.R.E (Contd.).
Mod-01 Lec-43 Frequency Domain Interpretation of LQR Controlled System.
Mod-01 Lec-44 Gain and Phase Margin of LQR Controlled System.
Mod-01 Lec-45 The Linear Quadratic Gaussian Problem.
Mod-01 Lec-46 Loop Transfer Recovery.
Mod-01 Lec-47 Dynamic Programming for Discrete Time System.
Mod-01 Lec-48 Minimum - Time Control of a Linear Time Invariant System.
Mod-01 Lec-49 Solution of Minimum - Time Control Problem with an Example.
Mod-01 Lec-50 Constraint in Control Inputs and State Variables.
Mod-01 Lec-51 Constraint in Control Inputs and State Variables (Contd.).
Mod-01 Lec-52 Norms for Vectors, Matrices, Signals and Linear Systems.
Mod-01 Lec-53 Signal and System Norms.
Mod-01 Lec-54 Internal Stability, Sensitivity and Complementary Sensitivity Functions.
Mod-01 Lec-55 Internal Stability, Sensitivity and Complementary Sensitivity Functions (Contd.).
Mod-01 Lec-56 Plant Uncertainty and Standard form for Robust Stability Analysis.
Mod-01 Lec-57 Plant Uncertainty and Standard form for Robust Stability Analysis (Contd.).
Mod-01 Lec-58 Frequency Response of Linear System and Singular Value Decomposition of System.
Mod-01 Lec-59 Control Problem Statement in H- alpha Framework.
Mod-01 Lec-60 Control Problem Statement in H - alpha Framework (Contd.).