Lecture 1 - Introduction to Optimization Problem: Some Examples Lecture 2 - Introduction to Optimization Problem: Some Examples (Continued.) Lecture 3 - Optimality Conditions for Function of Several Variables Lecture 4 - Optimality Conditions for Function of Several Variables (Continued.) Lecture 5 - Unconstrained Optimization Problem (Numerical Techniques) Lecture 6 - Solution of Unconstrained Optimization Problem Using Conjugate Quadient Method and Networks Methods Lecture 7 - Solution of Unconstrained Optimization Problem Using Conjugate Quadient Method and Networks Methods (Continued.) Lecture 8 - Solution of Constraint Optimization Problem-Karush-Kuhn Tucker (KKT) Conditions Lecture 9 - Solution of Constraint Optimization Problem-Karush-Kuhn Tucker (KKT) Conditions (Continued.) Lecture 10 - Problem and Solution Session Lecture 11 - Post Optimality Analysis, Convex Function and its Properties Lecture 12 - Post Optimality Analysis, Convex Function and its Properties (Continued.) Lecture 13 - Quadratic Optimization Problem Using Linear Programming Lecture 14 - Matrix form of the Simplex Method Lecture 15 - Matrix form of the Simplex Method (Continued.) Lecture 16 - Solution of Linear Programming Using Simplex Method:- Algebraic Approach Lecture 17 - Solution of Linear Programming Using Simplex Method:- Algebraic Approach (Continued.) Lecture 18 - Solution of LP Problems with Two Phase Method Lecture 19 - Solution of LP Problems with Two Phase Method (Continued.) Lecture 20 - Standard Primal and Dual Problems Lecture 21 - Relationship Between Primal and Dual Variables Lecture 22 - Solution of Quadratic Programming Problem Using Simplex Method Lecture 23 - Interior Point Method for Solving Optimization Problems Lecture 24 - Interior Point Method for Solving Optimization Problems (Continued.) Lecture 25 - Solution of Nonlinear Programming Problem Using Exterior Penalty Function Method Lecture 26 - Solution of Nonlinear Programming Problem Using Exterior Penalty Function Method (Continued.) Lecture 27 - Solution of Nonlinear Programming Problem Using Interior Penalty Function Method Lecture 28 - Solution of Nonlinear Programming Problem Using Interior Penalty Function Method (Continued.) Lecture 29 - Multiobjective Optimization Problem Lecture 30 - Dynamic Optimization Problem: Basic Concepts and Necessary and Sufficient Condition Lecture 31 - Dynamic Optimization Problem: Basic Concepts and Necessary and Sufficient Condition (Continued...1) Lecture 32 - Dynamic Optimization Problem: Basic Concepts and Necessary and Sufficient Condition (Continued...2) Lecture 33 - Numerical Example and Solution of Optimal Control Problem using Calculus of Variation principle Lecture 34 - Numerical Example and Solution of Optimal Control Problem using Calculus of Variation principle (Continued.) Lecture 35 - Hamiltonian Formulation for solution of optimal Control problem and numerical example Lecture 36 - Hamiltonian Formulation for solution of optimal Control problem and numerical example (Continued.) Lecture 37 - Performance Indices and Linear Quadratic Regulator Problem Lecture 38 - Performance Indices and Linear Quadratic Regulator Problem (Continued.) Lecture 39 - Solution and Stability Analysis of Finite - time LQR Problem: Numerical Example Lecture 40 - Solution and Infinite - time LQR Problem and Stability Analysis Lecture 41 - Numerical Example and Methods for Solution of A.R.E. Lecture 42 - Numerical Example and Methods for Solution of A.R.E. (Continued.) Lecture 43 - Frequency Domain Interpretation of LQR Controlled System Lecture 44 - Gain and Phase Margin of LQR Controlled System Lecture 45 - The Linear Quadratic Gaussian Problem Lecture 46 - Loop-Transfer Recovery Lecture 47 - Dynamic Programming for Discrete Time Systems Lecture 48 - Minimum – Time Control of a Linear Time Invariant System Lecture 49 - Solution of Minimum – Time Control Problem with an Example Lecture 50 - Constraint in Control Inputs and State Variables Lecture 51 - Constraint in Control Inputs and State Variables (Continued...) Lecture 52 - Norms for Vectors, Matrices, Signals and Linear Systems Lecture 53 - Signal and System Norms Lecture 54 - Internal Stability, Sensitivity and Complementary Sensitivity Functions Lecture 55 - Internal Stability, Sensitivity and Complementary Sensitivity Functions (Continued...) Lecture 56 - Plant Uncertainty and Standard form for Robust Stability Analysis Lecture 57 - Plant Uncertainty and Standard form for Robust Stability Analysis (Continued...) Lecture 58 - Frequency Response of Linear System and Singular Value Decomposition of System Lecture 59 - Control Problem Statement in H- alpha Framework Lecture 60 - Control Problem Statement in H - alpha Framework (Continued...)

Lecture 1 - Introduction to Optimization Problem: Some Examples Lecture 2 - Introduction to Optimization Problem: Some Examples (Continued.) Lecture 3 - Optimality Conditions for Function of Several Variables Lecture 4 - Optimality Conditions for Function of Several Variables (Continued.) Lecture 5 - Unconstrained Optimization Problem (Numerical Techniques) Lecture 6 - Solution of Unconstrained Optimization Problem Using Conjugate Quadient Method and Networks Methods Lecture 7 - Solution of Unconstrained Optimization Problem Using Conjugate Quadient Method and Networks Methods (Continued.) Lecture 8 - Solution of Constraint Optimization Problem-Karush-Kuhn Tucker (KKT) Conditions Lecture 9 - Solution of Constraint Optimization Problem-Karush-Kuhn Tucker (KKT) Conditions (Continued.) Lecture 10 - Problem and Solution Session Lecture 11 - Post Optimality Analysis, Convex Function and its Properties Lecture 12 - Post Optimality Analysis, Convex Function and its Properties (Continued.) Lecture 13 - Quadratic Optimization Problem Using Linear Programming Lecture 14 - Matrix form of the Simplex Method Lecture 15 - Matrix form of the Simplex Method (Continued.) Lecture 16 - Solution of Linear Programming Using Simplex Method:- Algebraic Approach Lecture 17 - Solution of Linear Programming Using Simplex Method:- Algebraic Approach (Continued.) Lecture 18 - Solution of LP Problems with Two Phase Method Lecture 19 - Solution of LP Problems with Two Phase Method (Continued.) Lecture 20 - Standard Primal and Dual Problems Lecture 21 - Relationship Between Primal and Dual Variables Lecture 22 - Solution of Quadratic Programming Problem Using Simplex Method Lecture 23 - Interior Point Method for Solving Optimization Problems Lecture 24 - Interior Point Method for Solving Optimization Problems (Continued.) Lecture 25 - Solution of Nonlinear Programming Problem Using Exterior Penalty Function Method Lecture 26 - Solution of Nonlinear Programming Problem Using Exterior Penalty Function Method (Continued.) Lecture 27 - Solution of Nonlinear Programming Problem Using Interior Penalty Function Method Lecture 28 - Solution of Nonlinear Programming Problem Using Interior Penalty Function Method (Continued.) Lecture 29 - Multiobjective Optimization Problem Lecture 30 - Dynamic Optimization Problem: Basic Concepts and Necessary and Sufficient Condition Lecture 31 - Dynamic Optimization Problem: Basic Concepts and Necessary and Sufficient Condition (Continued...1) Lecture 32 - Dynamic Optimization Problem: Basic Concepts and Necessary and Sufficient Condition (Continued...2) Lecture 33 - Numerical Example and Solution of Optimal Control Problem using Calculus of Variation principle Lecture 34 - Numerical Example and Solution of Optimal Control Problem using Calculus of Variation principle (Continued.) Lecture 35 - Hamiltonian Formulation for solution of optimal Control problem and numerical example Lecture 36 - Hamiltonian Formulation for solution of optimal Control problem and numerical example (Continued.) Lecture 37 - Performance Indices and Linear Quadratic Regulator Problem Lecture 38 - Performance Indices and Linear Quadratic Regulator Problem (Continued.) Lecture 39 - Solution and Stability Analysis of Finite - time LQR Problem: Numerical Example Lecture 40 - Solution and Infinite - time LQR Problem and Stability Analysis Lecture 41 - Numerical Example and Methods for Solution of A.R.E. Lecture 42 - Numerical Example and Methods for Solution of A.R.E. (Continued.) Lecture 43 - Frequency Domain Interpretation of LQR Controlled System Lecture 44 - Gain and Phase Margin of LQR Controlled System Lecture 45 - The Linear Quadratic Gaussian Problem Lecture 46 - Loop-Transfer Recovery Lecture 47 - Dynamic Programming for Discrete Time Systems Lecture 48 - Minimum – Time Control of a Linear Time Invariant System Lecture 49 - Solution of Minimum – Time Control Problem with an Example Lecture 50 - Constraint in Control Inputs and State Variables Lecture 51 - Constraint in Control Inputs and State Variables (Continued...) Lecture 52 - Norms for Vectors, Matrices, Signals and Linear Systems Lecture 53 - Signal and System Norms Lecture 54 - Internal Stability, Sensitivity and Complementary Sensitivity Functions Lecture 55 - Internal Stability, Sensitivity and Complementary Sensitivity Functions (Continued...) Lecture 56 - Plant Uncertainty and Standard form for Robust Stability Analysis Lecture 57 - Plant Uncertainty and Standard form for Robust Stability Analysis (Continued...) Lecture 58 - Frequency Response of Linear System and Singular Value Decomposition of System Lecture 59 - Control Problem Statement in H- alpha Framework Lecture 60 - Control Problem Statement in H - alpha Framework (Continued...)