Dynamic impulse systems: theory and applications
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English Macedonian |
| Published: |
Dordrecht [u.a.]
Kluwer
1997
|
| Series: | Mathematics and its applications
394 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 256 S. |
| ISBN: | 0792343948 |
Staff View
MARC
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| 100 | 1 | |a Zavališčin, Stanislav T. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Dynamic impulse systems |b theory and applications |c by S. T. Zavalishchin and A. N. Sesekin |
| 264 | 1 | |a Dordrecht [u.a.] |b Kluwer |c 1997 | |
| 300 | |a XI, 256 S. | ||
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface ix
1 ELEMENTS OF THE THEORY OF SCHWARTZ DISTRI¬
BUTIONS 1
1.1 Schwartz s notion of a distribution 1
1.2 Distributional derivatives 4
1.3 Convolution of distributions 7
1.4 The topology of the space V 10
1.5 Other classes of distributions 12
1.6 Linear equations in distributions 12
1.7 Convolution equations in distributions 14
2 EQUATIONS IN DISTRIBUTIONS: new approaches 15
2.1 Integral representations for distributions 16
2.1.1 Distributions depending on a parameter 16
2.1.2 Differentiation with respect to a parameter 17
2.1.3 Integration of distributions with respect to a parameter 18
2.1.4 Integral representations for distributions 22
2.1.5 A Cauchy Duhamel formula 23
2.2 Calculus of primitive distributions 26
2.2.1 Transforms of distributions and linear operations .... 26
2.2.2 Application to operator equations: common statements 31
2.3 Applications of calculus to linear equations of particular type . 34
2.3.1 Integral equations 34
2.3.2 Difference equations 35
2.3.3 Differential equations 36
2.3.4 Determination of the reaction of one dimensional con¬
trol systems to locally summable disturbance 42
2.3.5 Nonstationary convolution equations 46
2.4 Approaches to the construction problem of the general theory
of linear dynamic systems based on distributions theory .... 48
2.4.1 The problem statement 48
v
vi
2.4.2 Mathematical models of linear dynamic objects 49
2.4.3 Mathematical models of input output operators .... 51
2.5 Singular linear equations in distributions 59
2.5.1 Division of distributions by powers 59
2.5.2 Linear algebraic equations in distributions 61
2.5.3 Singular differential equation systems 63
2.6 Special nonlinear differential equations in distributions 74
2.6.1 Multiplication of discontinuous functions by impulse ones 74
2.6.2 Nonlinear differential equations in distributions. The
Frobenius case 77
2.6.3 Nonlinear differential equations in distributions. The
general case 81
3 APPLICATIONS TO PROBLEMS OF DYNAMICS AND
CONTROL 85
3.1 Banach Steinhaus lemma and the boundedness of integral op¬
erators 85
3.2 Topological characterization of stability 93
3.3 Discontinuous periodic motions of one dimensional nonlinear
systems with automatic regulation 97
3.4 Development of Barbashin s programming of given motions . . 104
3.5 Singular solutions of optimization problems for linear dynamic
systems with quadratic criteria 110
3.5.1 Optimal solutions of singularity order 1 Ill
3.5.2 Optimal solutions of singularity orders exceeding 1 ... 116
3.6 Singular solutions of optimization problems for nonlinear dy¬
namic systems 122
3.7 Programming the Bolza problem extremals with preassigned
dynamics 128
4 APPLIED CONTROL PROBLEMS 133
4.1 One link manipulators in a viscous medium 133
4.2 One link transport manipulators in a viscous medium 137
4.3 Two link manipulators in a viscous medium 142
4.4 Energy conserving algorithms for moving cylinders in a viscous
medium 146
4.5 Maximum radius orbit transfer in a given time 155
4.5.1 The problem statement 155
4.5.2 Variation of the final radius 158
4.5.3 Necassary conditions of optimality 160
4.6 Optimization of the kinetic energy of quantum objects 166
4.6.1 The problem statement 166
4.6.2 Solving Problem (AP) 169
4.6.3 Solving Problem (P) 170
vii
4.7 Applications to mathematical economics 173
4.7.1 Market mathematical models for discontinuous present
price 174
4.7.2 The stability of market equilibrium 175
4.7.3 Market optimization problems 177
5 DISCONTINUOUS SOLUTIONS TO ORDINARY NON¬
LINEAR DIFFERENTIAL EQUATIONS IN THE SPACE
OF FUNCTIONS OF BOUNDED VARIATION 179
5.1 Various ways to define generalized solutions to differential equa¬
tions 179
5.2 The space of functions of bounded variation 183
5.3 Definitions of discontinuous solutions 186
5.4 Approximable solutions and their estimates for bilinear inte¬
gral equations 187
5.5 V—solutions to nonlinear systems of differential equations . . . 194
5.5.1 Auxiliary differential equation 194
5.5.2 Integral inclusion for V—solutions 197
5.5.3 The case of unique V—solution 209
5.5.4 Examples 211
5.6 Approximable solutions to differential equations 213
5.6.1 Approximable solutions to nonlinear systems of differ¬
ential equations 213
5.6.2 A Cauchy formula for approximable solutions 216
5.6.3 Approximable solutions to n—order differential equations218
5.6.4 Discontinuous solutions to Lienard equation 221
5.6.5 Discontinuous solutions to neutral type differential
equations with time delay 226
6 PROPERTIES OF ATTAINABILITY SETS FOR DYNAMIC
SYSTEMS WITH DISCONTINUOUS TRAJECTORIES 231
6.1 Compactness of attainability sets 231
6.1.1 Closure of admissible controls set 231
6.1.2 Closure of the admissible trajectories set 234
6.2 Continuous dependence of attainability set on parameters . . . 236
6.2.1 Continuous dependence of attainability set on parame¬
ters in the right hand side of the system of differential
equations 237
6.2.2 Continuous dependence of attainability set on the mag¬
nitude of control resource 238
6.2.3 Continuity of the boundary of attainability set 240
6.3 Connectedness of the attainability set 241
6.4 Possible ways to construct the attainability set 245
6.5 Estimation on the number of impulses 246
References 248
Index 255
|
| any_adam_object | 1 |
| author | Zavališčin, Stanislav T. Sesekin, Aleksandr N. |
| author_facet | Zavališčin, Stanislav T. Sesekin, Aleksandr N. |
| author_role | aut aut |
| author_sort | Zavališčin, Stanislav T. |
| author_variant | s t z st stz a n s an ans |
| building | Verbundindex |
| bvnumber | BV011374830 |
| classification_rvk | SK 520 |
| classification_tum | MAT 496f MAT 910f MAT 344f |
| ctrlnum | (OCoLC)243862436 (DE-599)BVBBV011374830 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV011374830 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:08:40Z |
| institution | BVB |
| isbn | 0792343948 |
| language | English Macedonian |
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| physical | XI, 256 S. |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | Kluwer |
| record_format | marc |
| series | Mathematics and its applications |
| series2 | Mathematics and its applications |
| spelling | Zavališčin, Stanislav T. Verfasser aut Dynamic impulse systems theory and applications by S. T. Zavalishchin and A. N. Sesekin Dordrecht [u.a.] Kluwer 1997 XI, 256 S. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications 394 Dynamisches System (DE-588)4013396-5 gnd rswk-swf Optimierung (DE-588)4043664-0 gnd rswk-swf Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Dynamisches System (DE-588)4013396-5 s Numerisches Verfahren (DE-588)4128130-5 s DE-604 Optimierung (DE-588)4043664-0 s Sesekin, Aleksandr N. Verfasser aut Mathematics and its applications 394 (DE-604)BV008163334 394 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007644079&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Zavališčin, Stanislav T. Sesekin, Aleksandr N. Dynamic impulse systems theory and applications Mathematics and its applications Dynamisches System (DE-588)4013396-5 gnd Optimierung (DE-588)4043664-0 gnd Numerisches Verfahren (DE-588)4128130-5 gnd |
| subject_GND | (DE-588)4013396-5 (DE-588)4043664-0 (DE-588)4128130-5 |
| title | Dynamic impulse systems theory and applications |
| title_auth | Dynamic impulse systems theory and applications |
| title_exact_search | Dynamic impulse systems theory and applications |
| title_full | Dynamic impulse systems theory and applications by S. T. Zavalishchin and A. N. Sesekin |
| title_fullStr | Dynamic impulse systems theory and applications by S. T. Zavalishchin and A. N. Sesekin |
| title_full_unstemmed | Dynamic impulse systems theory and applications by S. T. Zavalishchin and A. N. Sesekin |
| title_short | Dynamic impulse systems |
| title_sort | dynamic impulse systems theory and applications |
| title_sub | theory and applications |
| topic | Dynamisches System (DE-588)4013396-5 gnd Optimierung (DE-588)4043664-0 gnd Numerisches Verfahren (DE-588)4128130-5 gnd |
| topic_facet | Dynamisches System Optimierung Numerisches Verfahren |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007644079&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008163334 |
| work_keys_str_mv | AT zavaliscinstanislavt dynamicimpulsesystemstheoryandapplications AT sesekinaleksandrn dynamicimpulsesystemstheoryandapplications |