---
# System prepended metadata

title: 'Lecture 04 : Continous Dynamic Programming'
tags: [Underactuated Robotics, Optimal Controls, MIT 6.832]

---

# Lecture 04 : Continous Dynamic Programming 

###### tags: `MIT 6.832` `Underactuated Robotics` `Optimal Controls`

These are my paper notes of Lecture 4 of the course MIT 6.832 (Underactuated Robotics) of 2019

**Youtube Channel :** [6.832 Underactuated Robotics](https://www.youtube.com/channel/UChfUOAhz7ynELF-s_1LPpWg/)
**Textbook :** [website](http://underactuated.csail.mit.edu/)
**Lecture :** [video](https://youtu.be/bMiiC94FJ5E)

# Table of Contents

[TOC]

## Topics covered 
* Continuous dynamic programming
    * The Hamilton-Jacobi-Bellman Equation
    * Solving for the minimizing control
    * Numerical solutions for $J^*$
* Linear Quadratic Regulators
    * Basic Derivation
        * Local stabilization of nonlinear systems
    * Finite-horizon formulations
    * Finite-horizon LQR

## Notes

![](https://i.imgur.com/8ObFcJD.jpg)
![](https://i.imgur.com/8zMEZNs.jpg)
![](https://i.imgur.com/JKcDAcY.jpg)
![](https://i.imgur.com/PZq4cw7.jpg)
![](https://i.imgur.com/nScPIzt.jpg)
