Modules / Lectures

- Introduction to Optimization
- Optimality Conditions for function of several variables
- Unconstrained optimization problem (Numerical Techniques)
- Solution of unconstarined optimization problem using conjugate gradient method and Newton\'s Method
- Solution of contraint optimization problems - karush - kuhn Tucker (KKT) conditions
- Problem Solution Session
- Post optimality analysis, convex function and its properties
- Quadratic optimization problem using Linear Programming
- Matrix form of the Simplex Method
- Solution of Linear Programming using Simplex Method - Algebraic Approach
- Solution of LP problems with Two - Phase Method
- Standard Primal and Dual problems
- Relationship between Primal and Dual Variables
- Solution of Quadratic Programming problem using Simplex Method
- Interior point method for solving optimization problems
- Solution Non linear Programming Problem using Exterior Penalty Function Method
- Solution of Non - linear Programming Problems using interior penalty function method
- Multi - variable optimization problem
- Dynamic Optimization Problem : Basic Concepts & Necessary and Sufficient Conditions
- Numerical Example and Solution of Optimal Control problem using Calculus of variation principle
- Hamiltonian Formulation for Solution of optimal control problem and numerical example
- Performance Indices and Linear Quadratic Regulator Problem
- Solution and stability analysis of finite - time LQR problem : Numerical Example
- Solution of Infinite - time LQR problem and stability analysis
- Numerical Example and Methods for Solution of A.R.E
- Frequency Domain Interpretation of LQR Controlled System
- Gain and Phase Margin of LQR Controlled System
- The Linear Quadratic Gaussian Problem
- Loop Transfer Recovery
- Dynamic Programming for Discrete Time System
- Minimum - Time Control of a Linear Time Invariant System
- Solution of Minimum - Time Control Problem with an Example
- Constraint in Control Inputs and State Variables
- Norms for Vectors, Matrices, Signals and Linear Systems
- Signal and System Norms
- Internal Stability, Sensitivity and Complementary Sensitivity Functions
- Plant Uncertainty and Standard form for Robust Stability Analysis
- Frequency Response of Linear System and Singular Value Decomposition of System
- Control Problem Statement in H- alpha Framework

Module Name | Download | Description | Download Size |
---|---|---|---|

Introduction to Optimization | Assignment | Please see all questions attached with the last module. | 37 kb |

Control Problem Statement in H- alpha Framework | Assignment | This is a questionnaire with answers that could be attempted after listening to the full course. | 148 kb |