Applied optimal control theory of distributed systems:
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| Previous Title: | Lurie, K. A. Optimal control in problems of mathematical physics |
|---|---|
| Main Author: | |
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Plenum Pr.
1993
|
| Series: | Mathematical concepts and methods in science and engineering
43 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 499 S. |
| ISBN: | 030643993X |
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MARC
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| 245 | 1 | 0 | |a Applied optimal control theory of distributed systems |c K. L. Lurie |
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Record in the Search Index
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| adam_text | Contents
1. Introduction 1
2. The Mayer Bolza Problem for Several Independent Variables:
Necessary Conditions for a Minimum 19
2.1. The Normal Form of the Basic Equations 19
2.2. General Scheme for Obtaining Necessary Conditions of Stationarity
and Realization of the Scheme for a Number of Special Cases . . 35
2.3. Weierstrass s Necessary Condition (Example) 51
2.4. Weierstrass s Necessary Condition (Continued): An Example . . 61
2.5. An Extremal Property of Strip Shaped Regions 69
2.6. The Case of Bounded Measurable Controls 75
2.7. Formula for the Increment of a Functional: Weierstrass s Necessary
Condition (the General Case) 80
2.8. Legendre s Necessary Condition 87
2.9. Jacobi s Necessary Condition 90
3. Optimal Distribution of the Resistivity of the Working Medium
in the Channel of a Magnetohydrodynamic Generator .... 93
3.1. Longitudinal End Effects in MHD Channels 93
3.2. Statement of the Problem (the Case of Scalar Resistivity) .... 103
3.3. Optimal Distributions of Scalar Resistivity 105
3.4. Effective Resistivity of Laminated Composites 118
3.5. Basic Equations in the Case of Tensorial Resistivity 122
3.6. Necessary Conditions for Stationarity (Tensor Case) 123
3.7. Weierstrass s Necessary Condition (Tensor Case) 126
3.8. The Asymptotic Case pmax » oo 134
3.9. Asymptotic Form of the Equations in the Optimal Range .... 136
3.10. Asymptotic Solution in the Range (j, grad co2) 0 138
3.11. Further Investigation of the Asymptotic Case: Existence of
Solution 154
3.12. Jacobi s Necessary Condition 173
ix
x Contents
3.13. Some Qualitative and Numerical Results 193
3.14. On a Class of Shape Optimization Problems: An Application of
Symmetrization 203
4. Relaxation of Optimization Problems with Equations Containing
the Operator V • D • V: An Application to the Problem of Elastic
Torsion 217
4.1. Problem Statement 218
4.2. Weak Convergence in Energy and Estimates of the Set GU . . . 223
4.3. G Closure of a Set U Consisting of Two Isotropic Plane Tensors
of the Second Rank (Problem I) 226
4.4. G Closure of a Set U Consisting of Symmetric Plane Tensors of
the Second Rank Possessing Different Orientations of the
Principal Axes (Problem II) 227
4.5. G Closure of a Set U Consisting of Two Arbitrary Plane
Symmetric Tensors of Rank Two 231
4.6. The General Case: G Closure of an Arbitrary Set of Symmetric
Plane Tensors of Rank Two 238
4.7. Elastic Bar of Extremal Torsional Rigidity: On the Existence of
Optimal Control 241
4.8. Necessary Conditions for Optimality 247
4.9. The Relaxed Optimal Torsion Problem 254
4.10. Necessary Conditions for Optimality within the Layers of
Laminated Composites 258
4.11. Some Numerical Results 260
5. Relaxation of Some Problems in the Optimal Design of Plates. . 265
5.1. Formulation of the Optimization Problem and of the Set of
Controls 267
5.2. Weierstrass s Necessary Conditions for Optimality 270
5.3. Contradictions within the Necessary Optimality Conditions . . . 272
5.4. The Effective Rigidity of a Laminated Composite 275
5.5. The Problem of G Closure: Estimation of the Set GU 278
5.5.1. Weak Convergence of the Strain Energy 278
5.5.2. Weak Convergence of the Second Strain Invariant 281
5.5.3. Estimates of the Effective Tensors D° in Terms of the Weak
Limit Tensors 283
5.5.4. The Case with Partly Known D° 285
5.6. G Closure of a Set U of Isotropic Materials with Equal Shear
Moduli and Different Dilatation Moduli 287
5.7. G Closure of a Set of Materials with Cubic Symmetry and Equal
Dilatation Moduli 292
Contents xi
5.8. Elimination of Contradictions Arising within Necessary Conditions
for Optimality 297
5.9. Problems of Optimal Thickness Design for Plates 300
6. Optimal Control of Systems Described by Equations of
Hyperbolic Type 305
6.1. Quasi linear First Order Equation 305
6.2. Example: A New Derivation of Bellman s Equation 314
6.3. An Optimization Problem for the Plastic Torsion of a Rod .... 318
6.4. Hyperbolic Optimization Problems for Regions Whose Boundaries
Contain Segments of Characteristics 328
6.5. The Optimal Shape of a Contour Surrounded by a Supersonic Gas
Flow 337
6.6. Necessary Conditions for Optimality in Quasi linear Hyperbolic
Systems with Fixed Principal Part 352
7. Parabolic and Other Evolution Optimization Problems .... 365
7.1. Optimal Heating of Bodies: Initial and Boundary Value Control • • 365
7.2. The Case When the Solution at a Finite Time Is Given 372
7.3. Optimal Relay Controls 376
7.4. Necessary Conditions for Optimality in Quasi linear Systems of
Parabolic Type 379
7.5. The Penalty Method . 389
7.6. Optimization Problems with Moving Boundaries 395
8. Bellman s Method in Variational Problems with Partial
Derivatives 401
8.1. Canonical Equations for the Simple Variational Problem with
Many Independent Variables: Volterra Form and Hadamard Levy
Form 402
8.2. The Hamilton Jacobi Equation for the Simple Variational Problem
with Partial Derivatives 407
8.3. The Hamilton Jacobi Method for the Simple Variational Problem
with Partial Derivatives 414
8.4. The Principle of Optimality 417
8.5. Bellman s Equation for Evolution Control Problems 418
8.6. Bellman s Equation for Elliptic Optimization Problems 423
8.7. Linear Systems: Quadratic Criterion 430
xii Contents
Appendix A: Calculations and Comments 441
Appendix B: Remarks and Guide to the Literature 463
References 471
Index 497
|
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| isbn | 030643993X |
| language | English |
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| physical | XII, 499 S. |
| publishDate | 1993 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
| publisher | Plenum Pr. |
| record_format | marc |
| series | Mathematical concepts and methods in science and engineering |
| series2 | Mathematical concepts and methods in science and engineering |
| spelling | Lurie, K. A. Verfasser aut Applied optimal control theory of distributed systems K. L. Lurie New York [u.a.] Plenum Pr. 1993 XII, 499 S. txt rdacontent n rdamedia nc rdacarrier Mathematical concepts and methods in science and engineering 43 Mathematische Physik Control theory Mathematical optimization Mathematical physics Mathematische Physik (DE-588)4037952-8 gnd rswk-swf Optimale Kontrolle (DE-588)4121428-6 gnd rswk-swf Optimale Kontrolle (DE-588)4121428-6 s Mathematische Physik (DE-588)4037952-8 s DE-604 Früher u.d.T. Lurie, K. A. Optimal control in problems of mathematical physics Mathematical concepts and methods in science and engineering 43 (DE-604)BV000001144 43 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007983106&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lurie, K. A. Applied optimal control theory of distributed systems Mathematical concepts and methods in science and engineering Mathematische Physik Control theory Mathematical optimization Mathematical physics Mathematische Physik (DE-588)4037952-8 gnd Optimale Kontrolle (DE-588)4121428-6 gnd |
| subject_GND | (DE-588)4037952-8 (DE-588)4121428-6 |
| title | Applied optimal control theory of distributed systems |
| title_auth | Applied optimal control theory of distributed systems |
| title_exact_search | Applied optimal control theory of distributed systems |
| title_full | Applied optimal control theory of distributed systems K. L. Lurie |
| title_fullStr | Applied optimal control theory of distributed systems K. L. Lurie |
| title_full_unstemmed | Applied optimal control theory of distributed systems K. L. Lurie |
| title_old | Lurie, K. A. Optimal control in problems of mathematical physics |
| title_short | Applied optimal control theory of distributed systems |
| title_sort | applied optimal control theory of distributed systems |
| topic | Mathematische Physik Control theory Mathematical optimization Mathematical physics Mathematische Physik (DE-588)4037952-8 gnd Optimale Kontrolle (DE-588)4121428-6 gnd |
| topic_facet | Mathematische Physik Control theory Mathematical optimization Mathematical physics Optimale Kontrolle |
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