Instructor:
Prof. Vadim Utkin
456 Dreese Laboratory
Phone: 292-6115
utkin@ee.eng.ohio-state.edu

Office Hours: To be arranged

Grading: Homework (4 total) 30%, Midterm 30%, Final Exam 40%

Textbook: Optimal Control Theory: an introduction, D. Kirk, Prentice-Hall, 1970.
This book is currently out of print. Relevant chapters will be made available in a Cop-Ez course package.

Prerequisites: EE 750 (Linear Systems Theory) or equivalent, or permission of instructor.

BRUTUS may still be checking outdated prerequisites. Any interested student who is denied registration or who does not meet the course prerequisite is urged to meet briefly with the instructor in order to check readiness and obtain permission for registration.

Course 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.

Outline: 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:

Optimality Problem in Control Theory
• Lecture 1:
  Introduction; Examples of optimality problems; The 'n-interval' theorem
• Lecture 2:
  Mathematical models; Classification of problem constraints
• Lecture 3:
  Conditions of optimality

The Calculus of Variations

• Lecture 4:
  Basic concepts; Variations of functionals; Extremals
• Lecture 5:
  Fundamental theorem of the calculus of variations; The Euler equation
• Lecture 6:
  Problems with constraints; Constraints of integral and boundary condition types; Differential equation constraints
• Lecture 7:
  Variational approach to optimal control; Costate equations; The Hamiltonian equation; Necessary conditions of optimality
• Lecture 8:
  Boundary conditions; Linear regulators

Pontryagin's Minimum Principle

• Lecture 9:
  The needle variation method
• Lecture 10:
  Minimum principle optimality conditions
• Lecture 11:
  Time-optimal and energy-optimal systems

Nonregular Cases

• Lecture 12:
  Singular optimal problems
• Lecture 13:
  Non-convex optimal problems; Optimal sliding modes

Dynamic Programming

• Lecture 14:
  Bellman's optimality principle
• Lecture 15:
  Discrete time systems
• Lecture 16:
  Continuous time systems; Bellman's function; The Hamilton-Jacobi-Bellman equation
• Lecture 17:
  Linear optimal systems; The Riccati equation; Singular problems
• Lecture 18:
  Review