590W: Applied Optimal Control and Estimation
Lectures: ARMS 1028, TTH 9:00-10:15 am
Professor Inseok Hwang
Office hours: TTH 10:15 - 11 am
system theory (AAE564/ECE602 or equivalent) and linear algebra (MA511
course is based on a set of lecture notes and articles which will be
available during the class.
main objective of this course is to study analysis and synthesis
optimal controllers and estimators for stochastic dynamical systems.
control is a time-domain method that computes the control input to a
system which minimizes a cost function. The dual problem is optimal
which computes the estimated states of the system with stochastic
by minimizing the errors between the true states and the estimated
Combination of the two leads to optimal stochastic control.
optimal stochastic control are to be found in science, economics, and
engineering. The course presents a review of mathematical background,
control and estimation, duality, and optimal stochastic control.
covered in this course:
- Review of some mathematical background
- Classical estimation
- Minimum variance unbiased estimation
- Least squares estimation
- Maximum likelihood estimation
- System Identification
- Optimal control
- Pontryagin’s Maximum/Minimum
- Hamilton-Jacobi-Bellman equation
- Dynamic Programming
- Linear Quadratic (LQR) problems
- Stochastic optimal control and
- Kalman Filter:
- Duality of LQR with Kalman filter
- Linear Quadratic
- B.D.O. Anderson and J. Moore, Optimal Control:
Linear Quadratic Methods, Prince Hall.
- A. Gelb, Applied optimal Estimation, MIT press.
- P. Maybeck, Stochastic
Models, Estimation, and Control, Academic Press
- L. Ljung, System Identification: Theory for the User, Prentice Hall.
- R. Stengel, Optimal Control and Estimation, Dover.
- R. Brown and P.
Hwang, Introduction to Random Signals and Applied Kalman
- A. E. Bryson and
Y.C. Ho, Applied Optimal Control.
- A couple of
problem sets per semester.
- No late homework
will be accepted.
projects could be an extension of existing algorithms in the literature
preferably, involve the original research ideas related to your current
research. Project should be chosen in consultation with Prof. Hwang.
schedule is as follows:
- Project Proposal
(two page summary) due March 26 (Thursday)
- Project report
(10-12 pages) due the dead week of classes
presentation: 15-minute presentation in the last week (before the final
proposal and report should be written in 11-size font with a single
- Homework 30%
- Class Project 70%
Class Materials (All class mtrerials will be
available in hard copies)