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# Optimal Control

## Syllabus

Mod-01 Lec-01 Introduction to Optimization.
Mod-01 Lec-02 Introduction to Optimization (Contd.).
Mod-01 Lec-03 Optimality Conditions for function of several variables.
Mod-01 Lec-04 Optimality Conditions for function of several variables (Contd.).
Mod-01 Lec-05 Unconstrained optimization problem (Numerical Techniques).
Mod-01 Lec-06 Solution of unconstarined optimization problem using conjugate gradient method.
Mod-01 Lec-07 Solution of unconstarined optimization problem using conjugate gradient method.
Mod-01 Lec-08 Solution of contraint optimization problems - karush - kuhn Tucker (KKT) conditions.
Mod-01 Lec-09 Solution of contraint optimization problems - karush - kuhn Tucker (KKT).
Mod-01 Lec-10 Problem Solution Session.
Mod-01 Lec-11 Post optimality analysis, convex function and its properties.
Mod-01 Lec-12 Post optimality analysis, convex function and its properties (Contd.).
Mod-01 Lec-13 Quadratic optimization problem using Linear Programming.
Mod-01 Lec-14 Matrix form of the Simplex Method.
Mod-01 Lec-15 Matrix form of the Simplex Method (Contd.).
Mod-01 Lec-16 Solution of Linear Programming using Simplex Method - Algebraic Approach.
Mod-01 Lec-17 Solution of Linear Programming using Simplex Method - Algebraic Approach (Contd.).
Mod-01 Lec-18 Solution of LP problems with Two - Phase Method.
Mod-01 Lec-19 Solution of LP problems with Two - Phase Method (Contd.).
Mod-01 Lec-20 Standard Primal and Dual problems.
Mod-01 Lec-21 Relationship between Primal and Dual Variables.
Mod-01 Lec-22 Solution of Quadratic Programming problem using Simplex Method.
Mod-01 Lec-23 Interior point method for solving optimization problems.
Mod-01 Lec-24 Interior point method for solving optimization problems (Contd.).
Mod-01 Lec-25 Solution Non linear Programming Problem using Exterior Penalty Function Method.
Mod-01 Lec-26 Solution Non linear Programming Problem using Exterior Penalty.
Mod-01 Lec-27 Solution of Non - linear Programming Problems using interior penalty function method.
Mod-01 Lec-28 Solution of Non - linear Programming Problems using interior penalty.
Mod-01 Lec-29 Multi - variable optimization problem.
Mod-01 Lec-30 Dynamic Optimization Problem : Basic Concepts & Necessary and Sufficient Conditions.
Mod-01 Lec-31 Dynamic Optimization Problem : Basic Concepts & Necessary and Sufficient.
Mod-01 Lec-32 Dynamic Optimization Problem : Basic Concepts & Necessary.
Mod-01 Lec-33 Numerical Example and Solution of Optimal Control problem.
Mod-01 Lec-34 Numerical Example and Solution of Optimal Control problem.
Mod-01 Lec-35 Hamiltonian Formulation for Solution of optimal control problem and numerical example.
Mod-01 Lec-36 Hamiltonian Formulation for Solution of optimal control problem.
Mod-01 Lec-37 Performance Indices and Linear Quadratic Regulator Problem.
Mod-01 Lec-38 Performance Indices and Linear Quadratic Regulator Problem (Contd.).
Mod-01 Lec-39 Solution and stability analysis of finite - time LQR problem : Numerical Example.
Mod-01 Lec-40 Solution of Infinite - time LQR problem and stability analysis.
Mod-01 Lec-41 Numerical Example and Methods for Solution of A.R.E.
Mod-01 Lec-42 Numerical Example and Methods for Solution of A.R.E (Contd.).
Mod-01 Lec-43 Frequency Domain Interpretation of LQR Controlled System.
Mod-01 Lec-44 Gain and Phase Margin of LQR Controlled System.
Mod-01 Lec-45 The Linear Quadratic Gaussian Problem.
Mod-01 Lec-46 Loop Transfer Recovery.
Mod-01 Lec-47 Dynamic Programming for Discrete Time System.
Mod-01 Lec-48 Minimum - Time Control of a Linear Time Invariant System.
Mod-01 Lec-49 Solution of Minimum - Time Control Problem with an Example.
Mod-01 Lec-50 Constraint in Control Inputs and State Variables.
Mod-01 Lec-51 Constraint in Control Inputs and State Variables (Contd.).
Mod-01 Lec-52 Norms for Vectors, Matrices, Signals and Linear Systems.
Mod-01 Lec-53 Signal and System Norms.
Mod-01 Lec-54 Internal Stability, Sensitivity and Complementary Sensitivity Functions.
Mod-01 Lec-55 Internal Stability, Sensitivity and Complementary Sensitivity Functions (Contd.).
Mod-01 Lec-56 Plant Uncertainty and Standard form for Robust Stability Analysis.
Mod-01 Lec-57 Plant Uncertainty and Standard form for Robust Stability Analysis (Contd.).
Mod-01 Lec-58 Frequency Response of Linear System and Singular Value Decomposition of System.
Mod-01 Lec-59 Control Problem Statement in H- alpha Framework.
Mod-01 Lec-60 Control Problem Statement in H - alpha Framework (Contd.).

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