On certain problems of the structure of ultrafilters related to extensions of abstract control problems
Abstract We study the procedures for constructing ultrafilters in measurable spaces that are in a general sense based on Cartesian products. Our constructions intend to use ultrafilters as generalized elements in extension constructions for abstract reachability problems with asymptotic constraints....
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Chentsov, A. G. [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2013 |
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| Schlagwörter: |
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| Anmerkung: |
© Pleiades Publishing, Ltd. 2013 |
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| Übergeordnetes Werk: |
Enthalten in: Automation and remote control - Springer US, 1957, 74(2013), 12 vom: Dez., Seite 2020-2036 |
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| Übergeordnetes Werk: |
volume:74 ; year:2013 ; number:12 ; month:12 ; pages:2020-2036 |
| Links: |
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| DOI / URN: |
10.1134/S0005117913120060 |
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OLC2060904951 |
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| 520 | |a Abstract We study the procedures for constructing ultrafilters in measurable spaces that are in a general sense based on Cartesian products. Our constructions intend to use ultrafilters as generalized elements in extension constructions for abstract reachability problems with asymptotic constraints. Constrains of this kind may arise, for instance, with sequential relaxation of boundary and intermediate conditions in control problems. In this case, families of sets of admissible regular controls in practically interesting cases represent filter bases, which makes it natural to use ultrafilters (maximal filters) that are admissible, in a certain sense, with respect to these families. We assume that counterparts of reachability sets considered in this work are sets in a topological space; the latter may be non-metrizable which occurs, for instance, in typical applications of the pointwise convergence topology. Such a topology may also be useful in impulse control problems, where one studies sheafs of motions as counterparts of reachability sets for exact and approximate satisfaction of trajectory constraints. | ||
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| 650 | 4 | |a Remote Control | |
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| 650 | 4 | |a Reachability Problem | |
| 650 | 4 | |a Reachability Region | |
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10.1134/S0005117913120060 doi (DE-627)OLC2060904951 (DE-He213)S0005117913120060-p DE-627 ger DE-627 rakwb eng 000 620 VZ Chentsov, A. G. verfasserin aut On certain problems of the structure of ultrafilters related to extensions of abstract control problems 2013 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Pleiades Publishing, Ltd. 2013 Abstract We study the procedures for constructing ultrafilters in measurable spaces that are in a general sense based on Cartesian products. Our constructions intend to use ultrafilters as generalized elements in extension constructions for abstract reachability problems with asymptotic constraints. Constrains of this kind may arise, for instance, with sequential relaxation of boundary and intermediate conditions in control problems. In this case, families of sets of admissible regular controls in practically interesting cases represent filter bases, which makes it natural to use ultrafilters (maximal filters) that are admissible, in a certain sense, with respect to these families. We assume that counterparts of reachability sets considered in this work are sets in a topological space; the latter may be non-metrizable which occurs, for instance, in typical applications of the pointwise convergence topology. Such a topology may also be useful in impulse control problems, where one studies sheafs of motions as counterparts of reachability sets for exact and approximate satisfaction of trajectory constraints. Control Problem Remote Control General Topology Reachability Problem Reachability Region Enthalten in Automation and remote control Springer US, 1957 74(2013), 12 vom: Dez., Seite 2020-2036 (DE-627)129603481 (DE-600)241725-X (DE-576)015097315 0005-1179 nnns volume:74 year:2013 number:12 month:12 pages:2020-2036 https://doi.org/10.1134/S0005117913120060 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-MAT GBV_ILN_70 AR 74 2013 12 12 2020-2036 |
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10.1134/S0005117913120060 doi (DE-627)OLC2060904951 (DE-He213)S0005117913120060-p DE-627 ger DE-627 rakwb eng 000 620 VZ Chentsov, A. G. verfasserin aut On certain problems of the structure of ultrafilters related to extensions of abstract control problems 2013 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Pleiades Publishing, Ltd. 2013 Abstract We study the procedures for constructing ultrafilters in measurable spaces that are in a general sense based on Cartesian products. Our constructions intend to use ultrafilters as generalized elements in extension constructions for abstract reachability problems with asymptotic constraints. Constrains of this kind may arise, for instance, with sequential relaxation of boundary and intermediate conditions in control problems. In this case, families of sets of admissible regular controls in practically interesting cases represent filter bases, which makes it natural to use ultrafilters (maximal filters) that are admissible, in a certain sense, with respect to these families. We assume that counterparts of reachability sets considered in this work are sets in a topological space; the latter may be non-metrizable which occurs, for instance, in typical applications of the pointwise convergence topology. Such a topology may also be useful in impulse control problems, where one studies sheafs of motions as counterparts of reachability sets for exact and approximate satisfaction of trajectory constraints. Control Problem Remote Control General Topology Reachability Problem Reachability Region Enthalten in Automation and remote control Springer US, 1957 74(2013), 12 vom: Dez., Seite 2020-2036 (DE-627)129603481 (DE-600)241725-X (DE-576)015097315 0005-1179 nnns volume:74 year:2013 number:12 month:12 pages:2020-2036 https://doi.org/10.1134/S0005117913120060 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-MAT GBV_ILN_70 AR 74 2013 12 12 2020-2036 |
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10.1134/S0005117913120060 doi (DE-627)OLC2060904951 (DE-He213)S0005117913120060-p DE-627 ger DE-627 rakwb eng 000 620 VZ Chentsov, A. G. verfasserin aut On certain problems of the structure of ultrafilters related to extensions of abstract control problems 2013 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Pleiades Publishing, Ltd. 2013 Abstract We study the procedures for constructing ultrafilters in measurable spaces that are in a general sense based on Cartesian products. Our constructions intend to use ultrafilters as generalized elements in extension constructions for abstract reachability problems with asymptotic constraints. Constrains of this kind may arise, for instance, with sequential relaxation of boundary and intermediate conditions in control problems. In this case, families of sets of admissible regular controls in practically interesting cases represent filter bases, which makes it natural to use ultrafilters (maximal filters) that are admissible, in a certain sense, with respect to these families. We assume that counterparts of reachability sets considered in this work are sets in a topological space; the latter may be non-metrizable which occurs, for instance, in typical applications of the pointwise convergence topology. Such a topology may also be useful in impulse control problems, where one studies sheafs of motions as counterparts of reachability sets for exact and approximate satisfaction of trajectory constraints. Control Problem Remote Control General Topology Reachability Problem Reachability Region Enthalten in Automation and remote control Springer US, 1957 74(2013), 12 vom: Dez., Seite 2020-2036 (DE-627)129603481 (DE-600)241725-X (DE-576)015097315 0005-1179 nnns volume:74 year:2013 number:12 month:12 pages:2020-2036 https://doi.org/10.1134/S0005117913120060 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-MAT GBV_ILN_70 AR 74 2013 12 12 2020-2036 |
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10.1134/S0005117913120060 doi (DE-627)OLC2060904951 (DE-He213)S0005117913120060-p DE-627 ger DE-627 rakwb eng 000 620 VZ Chentsov, A. G. verfasserin aut On certain problems of the structure of ultrafilters related to extensions of abstract control problems 2013 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Pleiades Publishing, Ltd. 2013 Abstract We study the procedures for constructing ultrafilters in measurable spaces that are in a general sense based on Cartesian products. Our constructions intend to use ultrafilters as generalized elements in extension constructions for abstract reachability problems with asymptotic constraints. Constrains of this kind may arise, for instance, with sequential relaxation of boundary and intermediate conditions in control problems. In this case, families of sets of admissible regular controls in practically interesting cases represent filter bases, which makes it natural to use ultrafilters (maximal filters) that are admissible, in a certain sense, with respect to these families. We assume that counterparts of reachability sets considered in this work are sets in a topological space; the latter may be non-metrizable which occurs, for instance, in typical applications of the pointwise convergence topology. Such a topology may also be useful in impulse control problems, where one studies sheafs of motions as counterparts of reachability sets for exact and approximate satisfaction of trajectory constraints. Control Problem Remote Control General Topology Reachability Problem Reachability Region Enthalten in Automation and remote control Springer US, 1957 74(2013), 12 vom: Dez., Seite 2020-2036 (DE-627)129603481 (DE-600)241725-X (DE-576)015097315 0005-1179 nnns volume:74 year:2013 number:12 month:12 pages:2020-2036 https://doi.org/10.1134/S0005117913120060 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-MAT GBV_ILN_70 AR 74 2013 12 12 2020-2036 |
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10.1134/S0005117913120060 doi (DE-627)OLC2060904951 (DE-He213)S0005117913120060-p DE-627 ger DE-627 rakwb eng 000 620 VZ Chentsov, A. G. verfasserin aut On certain problems of the structure of ultrafilters related to extensions of abstract control problems 2013 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Pleiades Publishing, Ltd. 2013 Abstract We study the procedures for constructing ultrafilters in measurable spaces that are in a general sense based on Cartesian products. Our constructions intend to use ultrafilters as generalized elements in extension constructions for abstract reachability problems with asymptotic constraints. Constrains of this kind may arise, for instance, with sequential relaxation of boundary and intermediate conditions in control problems. In this case, families of sets of admissible regular controls in practically interesting cases represent filter bases, which makes it natural to use ultrafilters (maximal filters) that are admissible, in a certain sense, with respect to these families. We assume that counterparts of reachability sets considered in this work are sets in a topological space; the latter may be non-metrizable which occurs, for instance, in typical applications of the pointwise convergence topology. Such a topology may also be useful in impulse control problems, where one studies sheafs of motions as counterparts of reachability sets for exact and approximate satisfaction of trajectory constraints. Control Problem Remote Control General Topology Reachability Problem Reachability Region Enthalten in Automation and remote control Springer US, 1957 74(2013), 12 vom: Dez., Seite 2020-2036 (DE-627)129603481 (DE-600)241725-X (DE-576)015097315 0005-1179 nnns volume:74 year:2013 number:12 month:12 pages:2020-2036 https://doi.org/10.1134/S0005117913120060 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-MAT GBV_ILN_70 AR 74 2013 12 12 2020-2036 |
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Abstract We study the procedures for constructing ultrafilters in measurable spaces that are in a general sense based on Cartesian products. Our constructions intend to use ultrafilters as generalized elements in extension constructions for abstract reachability problems with asymptotic constraints. Constrains of this kind may arise, for instance, with sequential relaxation of boundary and intermediate conditions in control problems. In this case, families of sets of admissible regular controls in practically interesting cases represent filter bases, which makes it natural to use ultrafilters (maximal filters) that are admissible, in a certain sense, with respect to these families. We assume that counterparts of reachability sets considered in this work are sets in a topological space; the latter may be non-metrizable which occurs, for instance, in typical applications of the pointwise convergence topology. Such a topology may also be useful in impulse control problems, where one studies sheafs of motions as counterparts of reachability sets for exact and approximate satisfaction of trajectory constraints. © Pleiades Publishing, Ltd. 2013 |
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Abstract We study the procedures for constructing ultrafilters in measurable spaces that are in a general sense based on Cartesian products. Our constructions intend to use ultrafilters as generalized elements in extension constructions for abstract reachability problems with asymptotic constraints. Constrains of this kind may arise, for instance, with sequential relaxation of boundary and intermediate conditions in control problems. In this case, families of sets of admissible regular controls in practically interesting cases represent filter bases, which makes it natural to use ultrafilters (maximal filters) that are admissible, in a certain sense, with respect to these families. We assume that counterparts of reachability sets considered in this work are sets in a topological space; the latter may be non-metrizable which occurs, for instance, in typical applications of the pointwise convergence topology. Such a topology may also be useful in impulse control problems, where one studies sheafs of motions as counterparts of reachability sets for exact and approximate satisfaction of trajectory constraints. © Pleiades Publishing, Ltd. 2013 |
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Abstract We study the procedures for constructing ultrafilters in measurable spaces that are in a general sense based on Cartesian products. Our constructions intend to use ultrafilters as generalized elements in extension constructions for abstract reachability problems with asymptotic constraints. Constrains of this kind may arise, for instance, with sequential relaxation of boundary and intermediate conditions in control problems. In this case, families of sets of admissible regular controls in practically interesting cases represent filter bases, which makes it natural to use ultrafilters (maximal filters) that are admissible, in a certain sense, with respect to these families. We assume that counterparts of reachability sets considered in this work are sets in a topological space; the latter may be non-metrizable which occurs, for instance, in typical applications of the pointwise convergence topology. Such a topology may also be useful in impulse control problems, where one studies sheafs of motions as counterparts of reachability sets for exact and approximate satisfaction of trajectory constraints. © Pleiades Publishing, Ltd. 2013 |
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<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">OLC2060904951</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230502215033.0</controlfield><controlfield tag="007">tu</controlfield><controlfield tag="008">200820s2013 xx ||||| 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1134/S0005117913120060</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)OLC2060904951</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-He213)S0005117913120060-p</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">000</subfield><subfield code="a">620</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Chentsov, A. G.</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">On certain problems of the structure of ultrafilters related to extensions of abstract control problems</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2013</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">ohne Hilfsmittel zu benutzen</subfield><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Band</subfield><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© Pleiades Publishing, Ltd. 2013</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract We study the procedures for constructing ultrafilters in measurable spaces that are in a general sense based on Cartesian products. Our constructions intend to use ultrafilters as generalized elements in extension constructions for abstract reachability problems with asymptotic constraints. Constrains of this kind may arise, for instance, with sequential relaxation of boundary and intermediate conditions in control problems. In this case, families of sets of admissible regular controls in practically interesting cases represent filter bases, which makes it natural to use ultrafilters (maximal filters) that are admissible, in a certain sense, with respect to these families. We assume that counterparts of reachability sets considered in this work are sets in a topological space; the latter may be non-metrizable which occurs, for instance, in typical applications of the pointwise convergence topology. Such a topology may also be useful in impulse control problems, where one studies sheafs of motions as counterparts of reachability sets for exact and approximate satisfaction of trajectory constraints.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Control Problem</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Remote Control</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">General Topology</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Reachability Problem</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Reachability Region</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Automation and remote control</subfield><subfield code="d">Springer US, 1957</subfield><subfield code="g">74(2013), 12 vom: Dez., Seite 2020-2036</subfield><subfield code="w">(DE-627)129603481</subfield><subfield code="w">(DE-600)241725-X</subfield><subfield code="w">(DE-576)015097315</subfield><subfield code="x">0005-1179</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:74</subfield><subfield code="g">year:2013</subfield><subfield code="g">number:12</subfield><subfield code="g">month:12</subfield><subfield code="g">pages:2020-2036</subfield></datafield><datafield tag="856" ind1="4" ind2="1"><subfield code="u">https://doi.org/10.1134/S0005117913120060</subfield><subfield code="z">lizenzpflichtig</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_OLC</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OLC-TEC</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OLC-MAT</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_70</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">74</subfield><subfield code="j">2013</subfield><subfield code="e">12</subfield><subfield code="c">12</subfield><subfield code="h">2020-2036</subfield></datafield></record></collection>
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