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Browse materialsMIT 16.323 · Spring 2008

Principles of Optimal Control

Art: Ottomar Anschütz, Lilienthal im unruhigen Gleitflug, 1894 · Public domain

Instructor: Prof. Jonathan P. How
Term: Spring 2008
Level: Graduate
What's inside: 2 exams · 2 solutions · 1 lecture note · 1 reading · 23 other files · 3 web pages
Materials open: MIT OCW

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About this course

Source: MIT OpenCourseWare 16.323 Principles of Optimal Control, Spring 2008, Prof. Jonathan P. How — original course page on ocw.mit.edu ↗. License: CC BY-NC-SA 4.0. Study order: MIT's own listing order, section by section. Taken from MIT's published course files, downloaded from ocw.mit.edu on September 23, 2026. How RedLectern is built.

Materials are grouped the way MIT organized them. A verified, course-wide order has not been established here.

Before you start

Prerequisites are not listed here. Check MIT's own syllabus for this course.

This course’s cited books, in our reading lists: Dynamic Programming and Optimal Control · Nonlinear Programming

How this course was organized

What's here, and what isn't

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Materials by section

Grouped by section, as MIT organized them. Not sequenced or ordered.

Lecture Notes

16 files

Assignments

Exams

MIT OpenCourseWare, Prof. Jonathan P. How, 16.323 Principles of Optimal Control, Spring 2008.

License: CC BY-NC-SA 4.0 · Edition: Spring 2008 · Open the original course on OCW ↗

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Principles of Optimal Control

Before you start

What's here, and what isn't

Not included here

Materials by section

Lecture Notes

Assignments

Exams

Lecture 1: Nonlinear optimization: unconstrained nonlinear optimization, line search methods

Lecture 2: Nonlinear optimization: constrained nonlinear optimization, Lagrange multipliers Penalty/barrier functions are also often used, but will not be discussed here.

Lecture 3: Dynamic programming: principle of optimality, dynamic programming, discrete LQR

Lecture 4: HJB equation: differential pressure in continuous time, HJB equation, continuous LQR

Lecture 5: Calculus of variations Most books cover this material well, but Kirk (chapter 4) does a particularly nice job. See here for an online reference.

Lecture 6: Calculus of variations applied to optimal control

Lecture 7: Numerical solution in MATLAB

Lecture 8: Properties of optimal control solution Bryson and Ho, Section 3.5 and Kirk, Section 4.4

Lecture 9: Constrained optimal control Bryson and Ho, section 3.x and Kirk, section 5.3

Lecture 10: Singular arcs Bryson, chapter 8 and Kirk, section 5.6

Lecture 11: Estimators/Observers Bryson, chapter 12 and Gelb, Optimal Estimation

Lecture 12: Stochastic optimal control Kwaknernaak and Sivan, chapters 3.6, 5; Bryson, chapter 14; and Stengel, chapter 5

Lecture 13: LQG robustness Stengel, chapter 6 Question: how well do the large gain and phase margins discussed for LQR (6-29) map over to LQG?

Lecture 14: 16.31 Feedback Control Systems: multiple-input multiple-output (MIMO) systems, singular value decomposition

Lecture 15: Signals and system norms: H∞ synthesis, different type of optimal controller

Lecture 16: Model predictive control