ME571 Homework

Lecture #	Topic
Optimality problem in Control Theory
1	Introduction. Examples. The 'n-interval' theorem
2	Mathematical Models. Classification of the Constraints.
3	Criteria of Optimality
Calculus of variations
4	Basic Concepts (variations of functionals, extremals)
5	Fundamental Theorem of Calculus of Variations. Euler Equation
6	Problems with Constraints (of integral and boundary condition type). Differential Equation
7	Variational Approach to Optimal Control. Costate Equations. Hamiltonian. Necessary Conditions of Optimality.
8	Boundary Conditions. Linear Regulators
Pontryagin's Minimum Principle
9	Needle Variation Method
10	Optimality Conditions
11	Time-Optimal Systems
Nonregular Cases
12	Singular Optimal Problems
13	Nonconvex Optimal Problems. Optimal Sliding Modes.
Dynamic Programming
14	Optimality Principle.
15	Discrete-Time Systems
16	Continuous-Time Systems. Bellman's Function. Hamilton-Jacobi-Bellman Equation.
17	Linear Optimal Systems. Riccati Equation. Singular Problems.
18	REVIEW

EE 854 Optimal Control Theory (07611-2) April, 2003 Time: Monday/Wednesday/Friday 11:30AM ~ 12:18PM Room: CL0135

Instructor	Vadim Utkin
Office	Dreese Lab 456 Phone: 292-6115 E-mail: utkin@ee.eng.ohio-state.edu
Pre-Requisite	EE750 or or equivalent, or permission of the instructor
Course Web Page	http://eewww.eng.ohio-state.edu/~utkin/EE854_Info.htm
Text Book	A.E. Bryson, Jr., Dynamic Optimization, Addison-Wesley, 1999
Office Hours	Monday/Wednesday 12:30PM~1:30PM
Grading	Homework: 30% Midterm: 30% (Click Midterm for further details) Final Exam: 40% (Click Final Exam for further details)
Homework	Homework assignments are due at the beginning of class. Homework assignments are either distributed in lecture or on this web page. (Click Homework for further details)
Solutions	Homework and Exam solutions will be placed either in class or on this web page.
Goals	The purpose of this course is to give students background in three historical trends in dynamic optimization: the Calculus of Variations, Pontryagin's Minimum Principle, and Bellman's Principle of Optimality. Not only will the underlying mathematics of the three principles be taught, but also their strengths and weaknesses - it is often less important to know how to apply a given principle than it is to know when. On a more immediate level this course will also prepare students to answer one of the four questions in the Control subsection of the M.S. Nonthesis/ Ph.D. Qualifying Examination. As stated in the departmental course description, topics to be covered include the three principles of optimality and their application to minimum time, energy, and fuel problems for continuous and discrete systems. A more thorough breakdown of Course Topics is as follows:

[EE 854 Homework]
Homework#1 (4/14)	Solution#1
Homework#2 (4/23)	Solution#2
Homework#3 (5/5)	Solution#3
Homework#4 (6/2)	Solution#4