Optimal control

The optimization techniques can be used in different ways depending on the approach (algebraic or geometric), the interest (single or multiple), the nature of the signals (deterministic or stochastic), and the stage (single or multiple). The main objective of optimal control is to determine control signals that will cause a process (plant) to satisfy some physical constraints and at the same time extremize (maximize or minimize) a chosen performance criterion (performance index or cost function).INTENDED AUDIENCE : It is an Elective Course forPG, Research Engineers, Scientists, Non Ph.D Faculties.PRE-REQUISITES : Advanced Control System.INDUSTRIES SUPPORT : DRDO, ISRO and Engineering Institutions etc.

Week 1 : Introduction and Performance Index Basic Concept of calculus of variation The basic variational problem Fixed end point problem Free end point problemWeek 2 : Free end point problem (Continued) Free end point problem (Continued) Free end point problem (Continued) Optimum of a function with conditions Optimum of Functions with Conditions (Lagrange Multiplier Method)Week 3 : Optimum of a functional with conditions Variational Approach to Optimal Control Systems Variational Approach to Optimal Control Systems (continued) Linear Quadratic Optimal Control Systems Linear Quadratic Optimal Control Systems (Contnued)Week 4 : Linear Quadratic Optimal Control Systems (Contnued) Linear Quadratic Optimal Control Systems (Contnued) Linear Quadratic Optimal Control Systems (Contnued) Linear Quadratic Optimal Control Systems (Optimal Value of Performance Index) Infinite Horizon Regulator ProblemWeek 5 : Infinite Horizon Regulator Problem (Continued) Analytical Solution of Matrix Differential Riccati Equation (State Transition Matrix Approach) Analytical Solution of Matrix Differential Riccati Equation (Similarity Transformation Approach) Analytical Solution of Matrix Differential Riccati Equation (Similarity Transformation Approach) (Continued) Frequency Domain Interpretation of LQR (Linear Time Invariant System)Week 6 : Frequency Domain Interpretation of LQR (Linear Time Invariant System) (Continued) LQR with a Specified Degree of Stability Inverse Matrix Riccati Equation Linear Quadratic Tracking System Discrete-Time Optimal Control SystemsWeek 7 : Discrete-Time Optimal Control Systems (Continued) Discrete-Time Optimal Control Systems (Continued) Matrix Discrete Riccati Equation Analytical Solution of Matrix Difference Riccati Equation Analytical Solution of Matrix Difference Riccati Equation (Continued)Week 8 : Optimal Control Using Dynamic Programming The Hamilton-Jacobi-Bellman (HJB) Equation LQR System Using H-J-B Equation Time Optimal Control System (Constrained Input) Time Optimal Control System(Continued)