文档介绍：An Introduction to Mathematical
Optimal Control Theory
Version
By
Lawrence C. Evans
Department of Mathematics
University of California, Berkeley
Chapter 1: Introduction
Chapter 2: Controllability, bang-bang principle
Chapter 3: Linear time-optimal control
Chapter 4: The Pontryagin Maximum Principle
Chapter 5: Dynamic programming
Chapter 6: Game theory
Chapter 7: Introduction to stochastic control theory
Appendix: Proofs of the Pontryagin Maximum Principle
Exercises
References
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PREFACE
These notes build upon a course I taught at the University of Maryland during
the fall of 1983. My great thanks go to Martino Bardi, who took careful notes,
saved them all these years and recently mailed them to me. Faye Yeager typed up
his notes into a first draft of these lectures as they now appear. Scott Armstrong
read over the notes and suggested many improvements: thanks, Scott. Stephen
Moye of the American Math Society helped me a lot with AMSTeX versus LaTeX
issues. My thanks also to Atilla Yilmaz for spotting lots of typos and errors, which
I have corrected.
I have radically modified much of the notation (to be consistent with my other
writings), updated the references, added several new examples, and provided a proof
of the Pontryagin Maximum Principle. As this is a course for undergraduates, I have
dispensed in certain proofs with various measurability and continuity issues, and as
compensation have added various critiques as to the lack of total rigor.
This current version of the notes is not plete, but meets I think the
usual high standards for material posted on the . Please email me at
******@ with any corrections ments.
2
CHAPTER 1: INTRODUCTION
. The basic problem
. Some examples
. A geometric solution
. Overview
THE BASIC PROBLEM.
DYNAMICS. We open our discussion by considering an ordinary differential
equation (ODE) having the form
x˙(t) = f(x(t)) (t > 0)
()
x(0) = x0