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Course10810501960 lectures

Optimal Control

Prof. G.D. Ray · IIT Kharagpur

Start with lecture 1 At NPTEL

Lectures

Introduction to Optimization

  1. Introduction to Optimization Video
  2. Introduction to Optimization (Contd.) Video

Optimality Conditions for function of several variables

  1. Optimality Conditions for function of several variables Video
  2. Optimality Conditions for function of several variables (Contd.) Video

Unconstrained optimization problem (Numerical Techniques)

  1. Unconstrained optimization problem (Numerical Techniques) Video

Solution of unconstarined optimization problem using conjugate gradient method and Newton\'s Method

  1. Solution of unconstarined optimization problem using conjugate gradient method and Newton's Method Video
  2. Solution of unconstarined optimization problem using conjugate gradient method and Newton's Method (Contd.) Video

Solution of contraint optimization problems - karush - kuhn Tucker (KKT) conditions

  1. Solution of contraint optimization problems - karush - kuhn Tucker (KKT) conditions Video
  2. Solution of contraint optimization problems - karush - kuhn Tucker (KKT) conditions (Contd.) Video

Problem Solution Session

  1. Problem Solution Session Video

Post optimality analysis, convex function and its properties

  1. Post optimality analysis, convex function and its properties Video
  2. Post optimality analysis, convex function and its properties (Contd.) Video

Quadratic optimization problem using Linear Programming

  1. Quadratic optimization problem using Linear Programming Video

Matrix form of the Simplex Method

  1. Matrix form of the Simplex Method Video
  2. Matrix form of the Simplex Method (Contd.) Video

Solution of Linear Programming using Simplex Method - Algebraic Approach

  1. Solution of Linear Programming using Simplex Method - Algebraic Approach Video
  2. Solution of Linear Programming using Simplex Method - Algebraic Approach (Contd.) Video

Solution of LP problems with Two - Phase Method

  1. Solution of LP problems with Two - Phase Method Video
  2. Solution of LP problems with Two - Phase Method (Contd.) Video

Standard Primal and Dual problems

  1. Standard Primal and Dual problems Video

Relationship between Primal and Dual Variables

  1. Relationship between Primal and Dual Variables Video

Solution of Quadratic Programming problem using Simplex Method

  1. Solution of Quadratic Programming problem using Simplex Method Video

Interior point method for solving optimization problems

  1. Interior point method for solving optimization problems Video
  2. Interior point method for solving optimization problems (Contd.) Video

Solution Non linear Programming Problem using Exterior Penalty Function Method

  1. Solution Non linear Programming Problem using Exterior Penalty Function Method Video
  2. Solution Non linear Programming Problem using Exterior Penalty Function Method (Contd.) Video

Solution of Non - linear Programming Problems using interior penalty function method

  1. Solution of Non - linear Programming Problems using interior penalty function method Video
  2. Solution of Non - linear Programming Problems using interior penalty function method (Contd.) Video

Multi - variable optimization problem

  1. Multi - variable optimization problem Video

Dynamic Optimization Problem : Basic Concepts & Necessary and Sufficient Conditions

  1. Dynamic Optimization Problem : Basic Concepts & Necessary and Sufficient Conditions Video
  2. Dynamic Optimization Problem : Basic Concepts & Necessary and Sufficient Conditions (Contd.) Video
  3. Dynamic Optimization Problem : Basic Concepts & Necessary and Sufficient Conditions (Contd.) Video

Numerical Example and Solution of Optimal Control problem using Calculus of variation principle

  1. Numerical Example and Solution of Optimal Control problem using Calculus of variation principle Video
  2. Numerical Example and Solution of Optimal Control problem using Calculus of variation principle (Contd.) Video

Hamiltonian Formulation for Solution of optimal control problem and numerical example

  1. Hamiltonian Formulation for Solution of optimal control problem and numerical example Video
  2. Hamiltonian Formulation for Solution of optimal control problem and numerical example (Contd.) Video

Performance Indices and Linear Quadratic Regulator Problem

  1. Performance Indices and Linear Quadratic Regulator Problem Video
  2. Performance Indices and Linear Quadratic Regulator Problem (Contd.) Video

Solution and stability analysis of finite - time LQR problem : Numerical Example

  1. Solution and stability analysis of finite - time LQR problem : Numerical Example Video

Solution of Infinite - time LQR problem and stability analysis

  1. Solution of Infinite - time LQR problem and stability analysis Video

Numerical Example and Methods for Solution of A.R.E

  1. Numerical Example and Methods for Solution of A.R.E Video
  2. Numerical Example and Methods for Solution of A.R.E (Contd.) Video

Frequency Domain Interpretation of LQR Controlled System

  1. Frequency Domain Interpretation of LQR Controlled System Video

Gain and Phase Margin of LQR Controlled System

  1. Gain and Phase Margin of LQR Controlled System Video

The Linear Quadratic Gaussian Problem

  1. The Linear Quadratic Gaussian Problem Video

Loop Transfer Recovery

  1. Loop Transfer Recovery Video

Dynamic Programming for Discrete Time System

  1. Dynamic Programming for Discrete Time System Video

Minimum - Time Control of a Linear Time Invariant System

  1. Minimum - Time Control of a Linear Time Invariant System Video

Solution of Minimum - Time Control Problem with an Example

  1. Solution of Minimum - Time Control Problem with an Example Video

Constraint in Control Inputs and State Variables

  1. Constraint in Control Inputs and State Variables Video
  2. Constraint in Control Inputs and State Variables (Contd.) Video

Norms for Vectors, Matrices, Signals and Linear Systems

  1. Norms for Vectors, Matrices, Signals and Linear Systems Video

Signal and System Norms

  1. Signal and System Norms Video

Internal Stability, Sensitivity and Complementary Sensitivity Functions

  1. Internal Stability, Sensitivity and Complementary Sensitivity Functions Video
  2. Internal Stability, Sensitivity and Complementary Sensitivity Functions (Contd.) Video

Plant Uncertainty and Standard form for Robust Stability Analysis

  1. Plant Uncertainty and Standard form for Robust Stability Analysis Video
  2. Plant Uncertainty and Standard form for Robust Stability Analysis (Contd.) Video

Frequency Response of Linear System and Singular Value Decomposition of System

  1. Frequency Response of Linear System and Singular Value Decomposition of System Video

Control Problem Statement in H- alpha Framework

  1. Control Problem Statement in H- alpha Framework Video
  2. Control Problem Statement in H - alpha Framework (Contd.) Video

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
IIT Kharagpur
Department
Electrical Engineering
Teacher
Prof. G.D. Ray
Level
Undergraduate
Language
English
Subjects
Engineering
Source
NPTEL
Licence
CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
Attribution
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