دانلود کتاب Introduction to the Theory of Systems

What is system theory? System theory is the study of systems. What, then, is a system? A system is best defined by what it does. It is a device or plant that receives inputs and transforms them into outputs which it gives out. Inputs and outputs form a very disparate class of objects.CONTENTS PHILOSOPHICAL INTRODUCTION 5 CHAPTER I - LINEAR SYSTEMS . 9 0 Introduction .. . . . . . . . . . 9 1 The "operation" of a linear system 9 2 Accessibility or controllability. . 11 3 Main theorem on accessibility . . 12 4 A more realistic point of view . . 14 5 Observability.......... . 15 CHAPTER II - THE CATEGORY OF SYSTEMS. . 18 0 Introduction .. . . . . . . . . . . . . 18 1 The feedback transformation groups . 19 2 Kronecker indices ." . 21 3 Partial canonical forms . 22 4 The normal form . . . . . 24 5 Relation with the holomorphic bundles on CP(l) . 27 6 Complex systems . . . . . . . . . . . . . . . . . . . 29 CHAPTER III - APPLICATIONS OF CONTROLLABILITY AND OBSERVABILITY .31 0 Pole assignment . 31 1 Stabilization . 33 2 Observers . . . 40 3 Asymptotic observers . 42 CHAPTER IV - NONLINEAR SYSTEMS .44 0 Introduction . . . . . . . . . 44 1 What is a general system? . . 44 2 Input-output mapping . . . 46 3 Examples of general systems . 47 4 Accessibility . . . . . . . . . . 49 5 Miscellany about accessibility . 51 6 Application to the attitude control of a satellite . 53 7 Local accessibility . . . . . . . . . . . . . . . . . 54 8 Local controllability of the satellite . . . . . . . . 56 APPENDIX TO CHAPTER IV - PROOF OF THE ORBIT THEOREM. . . . . . . . . . 58 CHAPTER V - OPTIMAL CONTROL THEORY . . 67 O Introduction to the problems of optimal control theory . 67 1 Some examples. . . . . . . . . . . . . . . . . . 68 2 The most famous problem in optimal control . 71 3 Necessary conditions in the LQC problem . . 72 4 Optimal control synthesis in the LQC case . . 76 5 The Ricatti equation . . . . . . . . . . . . . . 79 CHAPTER VI - OPTIMAL CONTROL - MAXIMUM PRINCIPLE . . . . . . . . 85 O Introduction . . . . . . . . . . . . . . 85 1 Statement of the maximum principle . 86 2 Applications . . . . . . . . . . . . . . 88 CHAPTER VII - PROOF OF THE MAXIMUM PRINCIPLE 95 O Approximating cones ........... . 95 1 The maximum principle in a special case. . 99 2 The general maximal principle 102 APPENDIX TO CHAPTER VII 104 REFERENCES . . . . . . . . . . 106