Lecture 29 of 60
Multi - variable optimization problem
Prof. G.D. Ray · IIT Kharagpur
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- Optimal Control, IIT Kharagpur (at NPTEL)
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All the lectures
- Introduction to Optimization
- Introduction to Optimization (Contd.)
- Optimality Conditions for function of several variables
- Optimality Conditions for function of several variables (Contd.)
- Unconstrained optimization problem (Numerical Techniques)
- Solution of unconstarined optimization problem using conjugate gradient method and Newton's Method
- Solution of unconstarined optimization problem using conjugate gradient method and Newton's Method (Contd.)
- Solution of contraint optimization problems - karush - kuhn Tucker (KKT) conditions
- Solution of contraint optimization problems - karush - kuhn Tucker (KKT) conditions (Contd.)
- Problem Solution Session
- Post optimality analysis, convex function and its properties
- Post optimality analysis, convex function and its properties (Contd.)
- Quadratic optimization problem using Linear Programming
- Matrix form of the Simplex Method
- Matrix form of the Simplex Method (Contd.)
- Solution of Linear Programming using Simplex Method - Algebraic Approach
- Solution of Linear Programming using Simplex Method - Algebraic Approach (Contd.)
- Solution of LP problems with Two - Phase Method
- Solution of LP problems with Two - Phase Method (Contd.)
- 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
- Interior point method for solving optimization problems (Contd.)
- Solution Non linear Programming Problem using Exterior Penalty Function Method
- Solution Non linear Programming Problem using Exterior Penalty Function Method (Contd.)
- Solution of Non - linear Programming Problems using interior penalty function method
- Solution of Non - linear Programming Problems using interior penalty function method (Contd.)
- Multi - variable optimization problem
- Dynamic Optimization Problem : Basic Concepts & Necessary and Sufficient Conditions
- Dynamic Optimization Problem : Basic Concepts & Necessary and Sufficient Conditions (Contd.)
- Dynamic Optimization Problem : Basic Concepts & Necessary and Sufficient Conditions (Contd.)
- Numerical Example and Solution of Optimal Control problem using Calculus of variation principle
- Numerical Example and Solution of Optimal Control problem using Calculus of variation principle (Contd.)
- Hamiltonian Formulation for Solution of optimal control problem and numerical example
- Hamiltonian Formulation for Solution of optimal control problem and numerical example (Contd.)
- Performance Indices and Linear Quadratic Regulator Problem
- Performance Indices and Linear Quadratic Regulator Problem (Contd.)
- 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
- Numerical Example and Methods for Solution of A.R.E (Contd.)
- 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
- Constraint in Control Inputs and State Variables (Contd.)
- Norms for Vectors, Matrices, Signals and Linear Systems
- Signal and System Norms
- Internal Stability, Sensitivity and Complementary Sensitivity Functions
- Internal Stability, Sensitivity and Complementary Sensitivity Functions (Contd.)
- Plant Uncertainty and Standard form for Robust Stability Analysis
- Plant Uncertainty and Standard form for Robust Stability Analysis (Contd.)
- Frequency Response of Linear System and Singular Value Decomposition of System
- Control Problem Statement in H- alpha Framework
- Control Problem Statement in H - alpha Framework (Contd.)