Limits of Localized Control in Extended Nonlinear Systems
نویسندگان
چکیده
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiv CHAPTER I — INTRODUCTION . . . . . . . . . . . . . . . . . . . . 1 1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.3 Systems under study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 CHAPTER II — CONTROL IN DYNAMICAL SYSTEMS . . . . . 9 2.1 Chaos control methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.2 Control theory methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 CHAPTER III — NONNORMALITY AND TRANSIENT GROWTH 19 3.1 Overview of nonnormality . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 3.2 The limitations of linear stability analysis . . . . . . . . . . . . . . . . . . 23 3.3 Characterization of nonnormality and transient growth . . . . . . . . . . . 28 3.4 Two toy models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 CHAPTER IV — LOCALIZED CONTROL OF EXTENDED SYSTEMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 4.1 Control at one boundary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 4.2 Control at both boundaries . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 4.3 Control at multiple locations . . . . . . . . . . . . . . . . . . . . . . . . . . 53 4.4 Control and nonnormality . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 CHAPTER V — TRANSIENT GROWTH IN THE CONTROLLED SYSTEM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 5.1 Scaling of the transient growth method I . . . . . . . . . . . . . . . . . . 66 5.2 Scaling of the transient growth method II . . . . . . . . . . . . . . . . . . 73 5.3 Scaling of the transient growth the sensing case . . . . . . . . . . . . . . 78
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