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Optimal Control

Optimal Control. Instructor: Prof. G. D. Ray, Department of Electrical Engineering, IIT Kharagpur. This course deal with topics in the static and dynamic optimization problems. An overview of optimization problem, some examples of optimum design problem. 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 unconstrained optimization problem. Solution of unconstrained optimization problem. Solution of constrained optimization problem using Karush-Kuhn-Tucker conditions. 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. (from nptel.ac.in)

Lecture 43 - Frequency Domain Interpretation of LQR Controlled System


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Lecture 01 - Introduction to Optimization
Lecture 02 - Introduction to Optimization (cont.)
Lecture 03 - Optimality Conditions for Function of Several Variables
Lecture 04 - Optimality Conditions for Function of Several Variables (cont.)
Lecture 05 - Unconstrained Optimization Problem (Numerical Techniques)
Lecture 06 - Solution of Unconstrained Optimization Problem using Conjugate Gradient Method and Newton's Method
Lecture 07 - Solution of Unconstrained Optimization Problem using Conjugate Gradient Method and Newton's Method (cont.)
Lecture 08 - Solution of Constraint Optimization Problem - Karush-Kuhn-Tucker Conditions
Lecture 09 - Solution of Constraint Optimization Problem - KKT Conditions (cont.)
Lecture 10 - Problem Solution Session
Lecture 11 - Post Optimality Analysis, Convex Function and its Properties
Lecture 12 - Post Optimality Analysis, Convex Function and its Properties (cont.)
Lecture 13 - Quadratic Optimization Problem using Linear Programming
Lecture 14 - Matrix Form of the Simplex Method
Lecture 15 - Matrix Form of the Simplex Method (cont.)
Lecture 16 - Solution of Linear Programming using Simplex Method - Algebraic Approach
Lecture 17 - Solution of Linear Programming using Simplex Method - Algebraic Approach (cont.)
Lecture 18 - Solution of Linear Programming Problems with Two-Phase Method
Lecture 19 - Solution of Linear Programming Problems with Two-Phase Method (cont.)
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 (cont.)
Lecture 25 - Solution of Nonlinear Programming Problem using Exterior Penalty Function Method
Lecture 26 - Solution of Nonlinear Programming Problem using Exterior Penalty Function Method (cont.)
Lecture 27 - Solution of Nonlinear Programming Problem using Interior Penalty Function Method
Lecture 28 - Solution of Nonlinear Programming Problem using Interior Penalty Function Method (cont.)
Lecture 29 - Multivariable Optimization Problem
Lecture 30 - Dynamic Optimization Problem: Basic Concepts, Necessary and Sufficient Conditions
Lecture 31 - Dynamic Optimization Problem: Basic Concepts, Necessary and Sufficient Conditions (cont.)
Lecture 32 - Dynamic Optimization Problem: Basic Concepts, Necessary and Sufficient Conditions (cont.)
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 (cont.)
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 (cont.)
Lecture 37 - Performance Indices and Linear Quadratic Regulator Problem
Lecture 38 - Performance Indices and Linear Quadratic Regulator Problem (cont.)
Lecture 39 - Solution and Stability Analysis of Finite-Time LQR Problem: Numerical Example
Lecture 40 - Solution of Infinite-Time LQR Problem and Stability Analysis
Lecture 41 - Numerical Example and Methods for Solution of Algebraic Recartic Equation
Lecture 42 - Numerical Example and Methods for Solution of ARE (cont.)
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 System
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 (cont.)
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 (cont.)
Lecture 56 - Plant Uncertainty and Standard Form for Robust Stability Analysis
Lecture 57 - Plant Uncertainty and Standard Form for Robust Stability Analysis (cont.)
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 (cont.)