top of page

EE 581:   Optimal  Control Systems

Graduate Course 


Office Hours :  Any time, please send an e-mail to :

Office No: 14-146-A

Office Location:  College of Engineering, Building 14.

Office Telephone:  ++ 973 17876286,  or  ++ 973 17876606

EE 581 :  Optimal  Control:    [3,1,3] : Calculus  of  Variations :

Basic concepts,  Fundamental theorem of the calculus of variations, 

The  Euler equation, 

Conditions of Optimality, 

The Hamiltonian.

Minimum Principle :

Pontrygain’s Principles, 

state constraints, 

Heaviside functions, 

Minimum principle optimality conditions.

Dynamic Programming

Bellman’s  optimality principle, 

Bellman’s function, 

The Hamilton-Jacobi-Bellman equation, 

Riccati Equation.

Optimal Dynamic Regulators.


Optimal regulators, 

and Stability analysis.

Optimal State Estimation

Optimality conditions, 

Kalman filters, 

and Optimal dynamic regulators.

LQG Systems

Separation principles, 

LQG systems, 

Tracking systems, 

LTR systems.

Prereq.  :  EE 580 :  Modern Control Systems


EE 581 Course :   Quality   Assurance  Office   Form 

Click to download and print the  College of Engineering  QAT  form of the  EE 581   ( for this semester )

Important  Charts  and  Tables  for  Control

Nichols Chart
Mp  and  Zeta relation
Overshoot and zeta relation
Second  Order  Frequency  Response



Course Marking-Assessment Distribution :

1 Assignments   (4 total ) 10%

2 Project  (Presentation)  05%

3 Labs 10%

4 Quizzes:   05%

5 Midterm  30%

6 Final  Exam40%


Course Text  Book : Textbook  :    Optimal Control  Theory  :  An introduction.     D.  Kirk,  Prentice-Hall,  1970.

You need to get my personal notes for this course.

Other References for this course is :
Modern Control Systems   (By :  R. Dorf and R. Bishop),                                               

Optimal  Control,  Theory and Applications     (By :  J.   Athens) ,                                    

Modern Control System Theory   ( By :  M. Gopal).

Control Simulation Software (You need to download) :

-  Matlab
-  Mathematica Control Toolbox
-  Codas
-  Vsim


Course LAB work  :  No Lab  for this course.

Course   Assignments  :  Assignments related to:

< >Assignment No. [1] : Introduction and Visualization of Control SystemAssignment No. [2] : Matlab and Simulink Introduction to Control StudentAssignment No. [3] :


Pontrygain’s Principles,  and the Optimality ConditionAssignment No. [4] : Dynamic Programming and the Hamilton-Jacobi-Bellman equationAssignment No. [5] : Dynamic Regulators.Assignment No. [6] : Raccti Based  Optimal Estimation and control systems.Assignment No. [7] : Optimal LQG  systems.Assignment No. [8] : Loop  Transfer  Recovery Controller for  a Multi-variable Control System.  This assignment is conducted with a presentation.  Course  Materials  Press to  (Download)  These topics will be provided by the  Instructor by  a Complete  Class  Notes

Optimal Control Introduction

Calculus  of  Variations

Minimum Principle

Pontrygain’s Principles

State Constraints

Heaviside Functions

Minimum Principle Optimality Conditions

Dynamic  Programming

The Hamilton-Jacobi-Bellman Equation

Optimal Dynamic Regulators

Optimal State Estimation  (Kalman Filtering)

LQG  (Linear  Quadratic  Gussaian)   Control Systems

Loop Transfer Recovery  Systems

Object Oriented Programming using Matlab (OOP):

Object Oriented Programming using Matlab (OOP), uses of classes (class), objects (obj) and data structure (struct) .. if you would like to use this approach in programming for this course, this will be great. This is optional, but it is always good to learn latest advanced programming tools.  Download slides about Matlab (oop), from the Advanced MATLAB for Scientific Computing, Stanford University.  (press here to download >>> )   OOP-Matlab

bottom of page