Mendeley出力
＜電子ブック＞
Introduction to the theory of differential inclusions
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| 目次 | Machine generated contents note: Part 1. Foundations Chapter 1. Convex Analysis 3 1.1. Convex sets 3 1.2. Convex functions 13 1.3. Differential properties of convex functions 24 1.4. Problems 30 Chapter 2. Set-Valued Analysis 31 2.1. Set-valued maps 31 2.2. Derivatives of set-valued maps 37 2.3. Lipschitzian approximations 41 2.4. Extension theorem 44 2.5. Fixed point theorems 47 2.6. Convex processes 49 2.7. Structure of a convex process 56 2.8. Problems 61 Chapter 3. Nonsmooth Analysis 65 3.1. Method of metric approximations 65 3.2. Mordukhovich normal cone 67 3.3. Separation theorem for nonconvex sets 72 3.4. Nonsmooth calculus 75 3.5. Lagrange multipliers 82 3.6. Problems 83 Part 2. Differential Inclusions Chapter 4. Existence Theorems 87 4.1. Background notes 88 4.2. Lipschitzian differential inclusions 90 4.3. Upper semi-continuous differential inclusions 96 4.4. Discontinuous differential equations 103 4.5. Existence of optimal solutions 106 4.6. Dependence on initial conditions 109 4.7. Discrete approximations 113 4.8. Problems 116 Chapter 5. Viability and Invariance 119 5.1. Monotone solutions to a differential inclusion 119 5.2. Viability problem 122 5.3. Invariant sets 127 5.4. Existence of periodic solutions 130 5.5. Pursuit in a differential game 132 5.6. Problems ' 135 Chapter 6. Controllability 139 6.1. Duality relation 139 6.2. Controllability of convex processes 145 6.3. Controllability at first approximation 147 6.4. Controllability of some mechanical systems 152 6.5. Problems 153 Chapter 7. Optimality 157 7.1. Optimal solutions to discrete-time inclusions 157 7.2. Optimal solutions to differential 4nclusions 160 7.3. Time-optimal problem 165 7.4. Problems 168 Chapter 8. Stability 171 8.1. Lyapunov direct method 171 8.2. Linear-selectionable differential inclusions 176 8.3. Weak asymptotic stability of convex processes 185 8.4. First approximation techniques 189 8.5. Stability of a missile uniform motion 194 8.6. Problems 196 Chapter 9. Stabilization 199 9.1. Lyapunov functions for convex processes 200 9.2. Stabilization problem 202 9.3. Weak asymptotic stability and stabilizability 205 9.4. Stabilizers for some mechanical systems 208 9.5. Problems 210.続きを見る |
| 冊子版へのリンク | https://hdl.handle.net/2324/1001226834 |
| 本文を見る | Graduate Studies in Mathematics - Electronic Backfile Collection (1993-2011): 2001 |
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| 登録日 | 2023.09.29 |
| 更新日 | 2024.01.30 |