TAILIEUCHUNG - AN INTRODUCTION TO MATHEMATICAL OPTIMAL CONTROL THEORY VERSION 0.1

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. | 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 1 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. 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. Scott Armstrong read over the notes and suggested many improvements thanks. This current version of the notes is not yet complete but meets I think the usual high standards for material posted on the internet. Please email me at evans@ with any corrections or comments. 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 x 0 x0. We are here given the initial point x0 G R and the function f R Rn. The unknown is the curve x 0 x Rn which we interpret as the dynamical evolution of the state of some system . 1-1 t 0 CONTROLLED DYNAMICS. We generalize a bit and suppose now that f depends also upon some .

• Toán học
• Controllability
• bang bang principle
• Game theory
• Dynamic programming
• stochastic control
• Pontryagin Maximum
• Interlocked feedback loop
• Flexible controllability
• Biological system
• Regulatory biological complex networks
• Interlocked positive feedback
• báo cáo hóa học
• công trình nghiên cứu về hóa học
• tài liệu về hóa học
• cách trình bày báo cáo
• báo cáo của tạp chí Vietnam Journal of Mathematics
• tài liệu báo cáo nghiên cứu khoa học
• kiến thức toán học
• báo cáo toán học
• Báo cáo sinh học hay
• báo cáo sinh học
• công trình nghiên cứu sinh học
• tài liệu về sinh học
• báo cáo khoa học
• Descriptor systems
• Controllability function
• State function
• Polynomial to find state function
• Differential algebraic equations
• BMC Bioinformatics
• Network analysis
• Systems biology
• Virus host interactions
• Influenza virus
• Information sciences
• Adding flexibility to uncertainty
• Flexible simple temporal networks
• Dynamic controllability
• Temporal constraint networks
• Flexible temporal networks
• Grid tie inverter
• DC link voltage regulator
• Maximum Power Point
• Severe operating
• Systematically performed
• Linear stationary Dynamic system
• Polynomial solutions
• Method cascade splitting
• Applied physics and engineering
• System consolidity
• Fuzzy theory and systems
• Superior consolidated systems
• Inferior consolidated systems
• System controllability