Optimal Control


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...)