Optimal Control Online Course, IIT Kharagpur http://freevideolectures.com 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 minimization problem using : Gradient descent method,Steepest descent method,Newton's method,Davison-Fletcher-Powell method,Exterior point method.

Numerical examples are considered to illustrate the algorithmic steps of the above methods - Solution of constrained minimization problems using Karush-Kuhn-Tucker (KKT) necessary and sufficient conditions - Numerical examples are considered to illustrate the technique.

Understanding the following terms : convex sets, convex and concave functions,properties of convex function,definiteness of a matrix and test for concavity of function,Explain with numerical examples.
Problem statement of : convex optimization,quadratic optimization,quadratically constrained quadratic optimization,local and global optima.

Solution of quadratic programming problems using KKT necessary condition - Basic concept of interior penalties and solution of convex optimization problem via interior point method - Numerical examples are considered to illustrate the techniques mentioned in Lec.-11 and Lec.12 - Linear programming: Simple method; matrix form of the simplex method - Illustrate the solution of linear programming problems in tabular form via simplex method - Two-phase simplex method - Primal and dual problem: Determination of primal solution from its dual form solution and vice-versa - Properties of dual problems and sensitivity analysis - Basic concept of multi-objective optimization problem and some definitions - Solution of multi-objective optimization problem and illustrate the methodoly with numerical examples.

Concept of functional, variational problems and performance indices - Euler-Lagrange equation to find the extremal of a functional. Transversality condition - Application of variation approach to control problems - Statement of Linear quadratic regulator (LQR) problem and establish a mathematical framework to solve this problem - Optimal solution of LQR problem - Different techniques for solution of algebraic Riccati equation.

Numerical problem are considered to illustrate the LQR design procedures and discussed the role of state and input weighting matrices on the system performance - Frequency domain interpretation of LQR problem - Stability and robustness properties of LQR design - Optimal control with constraints on input - Optimal saturating controllers - Dynamic programming principle of optimality - Concept of time optimal control problem and mathematical formulation of problem.

Solution of time-optimal control problem and explained with a numerical example - Concept of system and signal norms. Small-gain theorem, physical interpretation of H∞ norm - Computation of H∞ Norm, statement of H∞ control problem - H∞ control problem: Synthesis - Illustrative example - Discussion on stability margin and performance of H∞ based controlled systems. Optimal Control Online Course, IIT Kharagpur. Subscribed to the feed and get updated]]> Lecture 1: Mod-01 Lec-01 Introduction to Optimization Problem: Some Examples http://freevideolectures.com/Course/3081/Optimal-Control/1 Tue, 21 Aug 2012 00:00:00 -0600 Lecture 2: Mod-01 Lec-02 Introduction to Optimization Problem: Some Examples (Contd.) http://freevideolectures.com/Course/3081/Optimal-Control/2 Tue, 21 Aug 2012 00:00:00 -0600 Mod-01 Lec-03 Lecture-03-Optimality Conditions for Function of Several Variables http://freevideolectures.com/Course/3081/Optimal-Control/3 Tue, 21 Aug 2012 00:00:00 -0600 Mod-01 Lec-04 Lecture-04-Optimality Conditions for Function of Several Variables (Contd.) http://freevideolectures.com/Course/3081/Optimal-Control/4 Tue, 21 Aug 2012 00:00:00 -0600 Mod-01 Lec-05 Lecture-05-Unconstrained Optimization Problem (Numerical Techniques) http://freevideolectures.com/Course/3081/Optimal-Control/5 Tue, 21 Aug 2012 00:00:00 -0600 Lecture 6: Mod-01 Lec-06 Solution of Unconstrained Optimization Problem Using Conjugate Quadient Method http://freevideolectures.com/Course/3081/Optimal-Control/6 Tue, 21 Aug 2012 00:00:00 -0600 Lecture 7: Mod-01 Lec-07 Solution of Unconstrained Optimization Problem Using Conjugate Quadient http://freevideolectures.com/Course/3081/Optimal-Control/7 Tue, 21 Aug 2012 00:00:00 -0600 Lecture 8: Mod-01 Lec-08 Solution of Constraint Optimization Problem-Karush-Kuhn Tucker (KKT) Conditions http://freevideolectures.com/Course/3081/Optimal-Control/8 Tue, 21 Aug 2012 00:00:00 -0600 Mod-01 Lec-09 Lecture-09-Solution of Constraint Optimization Problem http://freevideolectures.com/Course/3081/Optimal-Control/9 Tue, 21 Aug 2012 00:00:00 -0600 Mod-01 Lec-10 Lecture-10-Problem and Solution Session http://freevideolectures.com/Course/3081/Optimal-Control/10 Tue, 21 Aug 2012 00:00:00 -0600 Lecture 11: Mod-01 Lec-11 Post Optimality Analysis, Convex Function and its Properties http://freevideolectures.com/Course/3081/Optimal-Control/11 Tue, 21 Aug 2012 00:00:00 -0600 Lecture 12: Mod-01 Lec-12 Post Optimality Analysis, Convex Function and its Properties (Contd.) http://freevideolectures.com/Course/3081/Optimal-Control/12 Tue, 21 Aug 2012 00:00:00 -0600 Lecture 13: Mod-01 Lec-13 Quadratic Optimization Problem Using Linear Programming http://freevideolectures.com/Course/3081/Optimal-Control/13 Tue, 21 Aug 2012 00:00:00 -0600 Mod-01 Lec-14 Lecture-14-Matrix form of the Simplex Method http://freevideolectures.com/Course/3081/Optimal-Control/14 Tue, 21 Aug 2012 00:00:00 -0600 Mod-01 Lec-15 Lecture-15-Matrix form of the Simplex Method (Contd.) http://freevideolectures.com/Course/3081/Optimal-Control/15 Tue, 21 Aug 2012 00:00:00 -0600 Lecture 16: Mod-01 Lec-16 Solution of Linear Programming Using Simplex Method:- Algebraic Approach http://freevideolectures.com/Course/3081/Optimal-Control/16 Tue, 21 Aug 2012 00:00:00 -0600 Lecture 17: Mod-01 Lec-17 Solution of Linear Programming Using Simplex Method:- Algebraic Approach (Contd.) http://freevideolectures.com/Course/3081/Optimal-Control/17 Tue, 21 Aug 2012 00:00:00 -0600 Lecture 18: Mod-01 Lec-18 Solution of LP Problems with Two Phase Method http://freevideolectures.com/Course/3081/Optimal-Control/18 Tue, 21 Aug 2012 00:00:00 -0600 Mod-01 Lec-19 Lecture-19-Solution of LP Problems with Two Phase Method (Contd.) http://freevideolectures.com/Course/3081/Optimal-Control/19 Tue, 21 Aug 2012 00:00:00 -0600 Mod-01 Lec-20 Lecture-20-Standard Primal and Dual Problems http://freevideolectures.com/Course/3081/Optimal-Control/20 Tue, 21 Aug 2012 00:00:00 -0600 Lecture 21: Mod-01 Lec-21 Relationship Between Primal and Dual Variables http://freevideolectures.com/Course/3081/Optimal-Control/21 Tue, 21 Aug 2012 00:00:00 -0600 Lecture 22: Mod-01 Lec-22 Solution of Quadratic Programming Problem Using Simplex Method http://freevideolectures.com/Course/3081/Optimal-Control/22 Tue, 21 Aug 2012 00:00:00 -0600 Lecture 23: Mod-01 Lec-23 Interior Point Method for Solving Optimization Problems http://freevideolectures.com/Course/3081/Optimal-Control/23 Tue, 21 Aug 2012 00:00:00 -0600 Mod-01 Lec-24 Lecture-24-Interior Point Method for Solving Optimization Problems (Contd.) http://freevideolectures.com/Course/3081/Optimal-Control/24 Tue, 21 Aug 2012 00:00:00 -0600 Mod-01 Lec-25 Lecture-25-Solution of Nonlinear Programming Problem http://freevideolectures.com/Course/3081/Optimal-Control/25 Tue, 21 Aug 2012 00:00:00 -0600 Lecture 26: Mod-01 Lec-26 Solution of Nonlinear Programming Problem Using Exterior Penalty http://freevideolectures.com/Course/3081/Optimal-Control/26 Tue, 21 Aug 2012 00:00:00 -0600 Lecture 27: Mod-01 Lec-27 Solution of Nonlinear Programming Problem Using Interior Penalty Function Method http://freevideolectures.com/Course/3081/Optimal-Control/27 Tue, 21 Aug 2012 00:00:00 -0600 Lecture 28: Mod-01 Lec-28 Solution of Nonlinear Programming Problem Using Interior Penalty Fun Mthd (Contd.) http://freevideolectures.com/Course/3081/Optimal-Control/28 Tue, 21 Aug 2012 00:00:00 -0600 Mod-01 Lec-29 Lecture-29-Multiobjective Optimization Problem http://freevideolectures.com/Course/3081/Optimal-Control/29 Tue, 21 Aug 2012 00:00:00 -0600 Mod-01 Lec-30 Lecture-30-Dynamic Optimization Problem: http://freevideolectures.com/Course/3081/Optimal-Control/30 Tue, 21 Aug 2012 00:00:00 -0600 Lecture 31: Mod-01 Lec-31 Dynamic Optimization Problem: Basic Concepts and Necessary (cont.,) http://freevideolectures.com/Course/3081/Optimal-Control/31 Tue, 21 Aug 2012 00:00:00 -0600 Mod-01 Lec-32 Lecture-32-Dynamic Optimization Problem: http://freevideolectures.com/Course/3081/Optimal-Control/32 Tue, 21 Aug 2012 00:00:00 -0600 Mod-01 Lec-33 Lecture-33-Numerical Example and Solution of Optimal Control Problem http://freevideolectures.com/Course/3081/Optimal-Control/33 Tue, 21 Aug 2012 00:00:00 -0600 Mod-01 Lec-34 Lecture-34-Numerical Example and Solution of Optimal Control Problem http://freevideolectures.com/Course/3081/Optimal-Control/34 Tue, 21 Aug 2012 00:00:00 -0600 Mod-01 Lec-35 Lecture-35-Hamiltonian Formulation for solution of optimal Control problem http://freevideolectures.com/Course/3081/Optimal-Control/35 Tue, 21 Aug 2012 00:00:00 -0600 Lecture 36: Mod-01 Lec-36 Hamiltonian Formulation for solution of optimal Control problem(Contd.) http://freevideolectures.com/Course/3081/Optimal-Control/36 Tue, 21 Aug 2012 00:00:00 -0600 Mod-01 Lec-37 Lecture-37-Performance Indices and Linear Quadratic Regulator Problem http://freevideolectures.com/Course/3081/Optimal-Control/37 Tue, 21 Aug 2012 00:00:00 -0600 Mod-01 Lec-38 Lecture-38-Performance Indices and Linear Quadratic Regulator Problem (Contd.) http://freevideolectures.com/Course/3081/Optimal-Control/38 Tue, 21 Aug 2012 00:00:00 -0600 Mod-01 Lec-39 Lecture-39-Solution and Stability Analysis of Finite - time LQR Problem: http://freevideolectures.com/Course/3081/Optimal-Control/39 Tue, 21 Aug 2012 00:00:00 -0600 Mod-01 Lec-40 Lecture-40-Solution and Infinite - time LQR Problem and Stability Analysis http://freevideolectures.com/Course/3081/Optimal-Control/40 Tue, 21 Aug 2012 00:00:00 -0600 Lecture 41: Mod-01 Lec-41 Numerical Example and Methods for Solution of A.R.E. http://freevideolectures.com/Course/3081/Optimal-Control/41 Tue, 21 Aug 2012 00:00:00 -0600 Mod-01 Lec-42 Lecture-42-Numerical Example and Methods for Solution of A.R.E. (Contd.) http://freevideolectures.com/Course/3081/Optimal-Control/42 Tue, 21 Aug 2012 00:00:00 -0600 Mod-01 Lec-43 Lecture-43-Frequency Domain Interpretation of LQR Controlled System http://freevideolectures.com/Course/3081/Optimal-Control/43 Tue, 21 Aug 2012 00:00:00 -0600 Mod-01 Lec-44 Lecture-44-Gain and Phase Margin of LQR Controlled System http://freevideolectures.com/Course/3081/Optimal-Control/44 Tue, 21 Aug 2012 00:00:00 -0600 Lecture 45: Mod-01 Lec-45 The Linear Quadratic Gaussian Problem http://freevideolectures.com/Course/3081/Optimal-Control/45 Tue, 21 Aug 2012 00:00:00 -0600 Lecture 46: Mod-01 Lec-46 Loop-Transfer Recovery http://freevideolectures.com/Course/3081/Optimal-Control/46 Tue, 21 Aug 2012 00:00:00 -0600 Mod-01 Lec-47 Lecture-47-Dynamic Programming for Discrete Time Systems http://freevideolectures.com/Course/3081/Optimal-Control/47 Tue, 21 Aug 2012 00:00:00 -0600 Mod-01 Lec-48 Lecture-48-Minimum -- Time Control of a Linear Time Invariant System http://freevideolectures.com/Course/3081/Optimal-Control/48 Tue, 21 Aug 2012 00:00:00 -0600 Mod-01 Lec-49 Lecture-49-Solution of Minimum -- Time Control Problem with an Example http://freevideolectures.com/Course/3081/Optimal-Control/49 Tue, 21 Aug 2012 00:00:00 -0600