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Course Description

Optimal control deals with the problem of finding a control law for a given system such that a certain optimality criterion is achieved. A control problem includes a cost functional that is a function of state and control variables. An optimal control is a set of differential equations describing the paths of the control variables that minimize the cost functional. The optimal control can be derived using Pontryagin's maximum principle (a necessary condition also known as Pontryagin's minimum principle or simply Pontryagin's Principle[2]), or by solving the Hamilton–Jacobi–Bellman equation (a sufficient condition).

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Course Syllabus
  • Mod-01 Lec-01 Introduction, Motivation and Overview
  • Mod-01 Lec-02 Overview of SS Approach and Matrix Theory
  • Mod-01 Lec-03 Review of Numerical Methods
  • Mod-02 Lec-04 An Overview of Static Optimization -- I
  • Mod-02 Lec-05 An Overview of Static Optimization -- II
  • Mod-03 Lec-06 Review of Calculus of Variations -- I
  • Mod-03 Lec-07 Review of Calculus of Variations -- II
  • Mod-03 Lec-08 Optimal Control Formulation Using Calculus of Variations
  • Mod-04 Lec-09 Classical Numerical Methods to Solve Optimal Control Problems
  • Mod-05 Lec-10 Linear Quadratic Regulator (LQR) -- I
  • Mod-05 Lec-11 Linear Quadratic Regulator (LQR) -- II
  • Mod-05 Lec-12 Linear Quadratic Regulator (LQR) -- III
  • Mod-05 Lec-13 Linear Quadratic Regulator (LQR) -- III
  • Mod-06 Lec-14 Discrete-time Optimal Control
  • Mod-07 Lec-15 Overview of Flight Dynamics -- I
  • Mod-07 Lec-16 Overview of Flight Dynamics -- II
  • Mod-07 Lec-17 Overview of Flight Dynamics -- III
  • Mod-08 Lec-18 Linear Optimal Missile Guidance using LQR
  • Mod-09 Lec-19 SDRE and θ -- D Designs
  • Mod-10 Lec-20 Dynamic Programming
  • Mod-10 Lec-21 Approximate Dynamic Progr (ADP),Adaptive Critic (AC)
  • Mod-11 Lec-22 Transcription Method to Solve Optimal Control Problems
  • Mod-11 Lec-23 Model Predictive Static Programming (MPSP) and Optimal Guidance of Aerospace Vehicles
  • Mod-11 Lec-24 MPSP for Optimal Missile Guidance
  • Mod-11 Lec-25 Model Predictive Spread Control (MPSC) and Generalized MPSP (G-MPSP) Designs
  • Mod-12 Lec-26 Linear Quadratic Observer & An Overview of State Estimation
  • Mod-12 Lec-27 Review of Probability Theory and Random Variables
  • Mod-12 Lec-28 Kalman Filter Design -- I
  • Mod-12 Lec-29 Kalman Filter Design -- II
  • Mod-12 Lec-30 Kalman Filter Design -- III
  • Mod-13 Lec-31 Integrated Estimation, Guidance & Control -- I
  • Mod-13 Lec-32 Integrated Estimation, Guidance & Control -- II
  • Mod-14 Lec-33 LQG Design; Neighboring Optimal Control & Sufficiency Condition
  • Mod-15 Lec-34 Constrained Optimal Control -- I
  • Mod-15 Lec-35 Constrained Optimal Control -- II
  • Mod-15 Lec-36 Constrained Optimal Control -- III
  • Mod-16 Lec-37 Optimal Control of Distributed Parameter Systems -- I
  • Mod-16 Lec-38 Optimal Control of Distributed Parameter Systems -- II
  • Mod-17 Lec-39 Take Home Material: Summary -- I
  • Mod-17 Lec-40 Take Home Material: Summary -- I

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