A singular control approach to highly damped second-order abstract equations and applications View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

1997-07

AUTHORS

I. Lasiecka, L. Pandolfi, R. Triggiani

ABSTRACT

In this paper we restudy, by a radically different approach, the optimal quadratic cost problem for an abstract dynamics, which models a special class of second-order partial differential equations subject to high internal damping and acted upon by boundary control. A theory for this problem was recently derived in [LLP] and [T1] (see also [T2]) by a change of variable method and by a direct approach, respectively. Unlike [LLP] and [T1], the approach of the present paper is based on singular control theory, combined with regularity theory of the optimal pair from [T1]. This way, not only do we rederive the basic control-theoretic results of [LLP] and [T1]—the (first) synthesis of the optimal pair, and the (first) nonstandard algebraic Riccati equation for the (unique) Riccati operator which enters into the gain operator of the synthesis—but in addition, this method also yields new results—a second form of the synthesis of the optimal pair, and a second (still nonstandard) algebraic Riccati equation for the (still unique) Riccati operator of the synthesis. These results, which show new pathologies in the solution of the problem, are new even in the finite-dimensional case. More... »

PAGES

67-107

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/bf02683338

DOI

http://dx.doi.org/10.1007/bf02683338

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1029693830


Indexing Status Check whether this publication has been indexed by Scopus and Web Of Science using the SN Indexing Status Tool
Incoming Citations Browse incoming citations for this publication using opencitations.net

JSON-LD is the canonical representation for SciGraph data.

TIP: You can open this SciGraph record using an external JSON-LD service: JSON-LD Playground Google SDTT

[
  {
    "@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json", 
    "about": [
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0101", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Pure Mathematics", 
        "type": "DefinedTerm"
      }, 
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/01", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Mathematical Sciences", 
        "type": "DefinedTerm"
      }
    ], 
    "author": [
      {
        "affiliation": {
          "alternateName": "University of Virginia", 
          "id": "https://www.grid.ac/institutes/grid.27755.32", 
          "name": [
            "Department of Applied Mathematics, Thornton Hall, University of Virginia, 22903, Charlottesville, VA, USA"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Lasiecka", 
        "givenName": "I.", 
        "id": "sg:person.011122656703.80", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.011122656703.80"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Polytechnic University of Turin", 
          "id": "https://www.grid.ac/institutes/grid.4800.c", 
          "name": [
            "Dipartimento di Matematica, Politecnico di Torino, Corso Duca degli Abruzzi, 24, 10129, Torino, Italy"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Pandolfi", 
        "givenName": "L.", 
        "id": "sg:person.012351424331.97", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012351424331.97"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "University of Virginia", 
          "id": "https://www.grid.ac/institutes/grid.27755.32", 
          "name": [
            "Department of Applied Mathematics, Thornton Hall, University of Virginia, 22903, Charlottesville, VA, USA"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Triggiani", 
        "givenName": "R.", 
        "id": "sg:person.01303304750.12", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01303304750.12"
        ], 
        "type": "Person"
      }
    ], 
    "citation": [
      {
        "id": "https://doi.org/10.1016/0022-247x(70)90283-0", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1010506843"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf01182784", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1021021835", 
          "https://doi.org/10.1007/bf01182784"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf01182784", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1021021835", 
          "https://doi.org/10.1007/bf01182784"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf01442189", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1030856017", 
          "https://doi.org/10.1007/bf01442189"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf01442189", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1030856017", 
          "https://doi.org/10.1007/bf01442189"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf01776850", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1031864845", 
          "https://doi.org/10.1007/bf01776850"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf01776850", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1031864845", 
          "https://doi.org/10.1007/bf01776850"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf02191985", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1037971054", 
          "https://doi.org/10.1007/bf02191985"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf02191985", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1037971054", 
          "https://doi.org/10.1007/bf02191985"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-1-4612-5561-1", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1042930842", 
          "https://doi.org/10.1007/978-1-4612-5561-1"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-1-4612-5561-1", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1042930842", 
          "https://doi.org/10.1007/978-1-4612-5561-1"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1137/0321003", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1062843669"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1137/0325035", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1062843959"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1137/0330058", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1062844386"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1137/0523022", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1062848435"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bfb0006880", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1109719076", 
          "https://doi.org/10.1007/bfb0006880"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bfb0006880", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1109719076", 
          "https://doi.org/10.1007/bfb0006880"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bfb0006880", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1109719076", 
          "https://doi.org/10.1007/bfb0006880"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bfb0006880", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1109719076", 
          "https://doi.org/10.1007/bfb0006880"
        ], 
        "type": "CreativeWork"
      }
    ], 
    "datePublished": "1997-07", 
    "datePublishedReg": "1997-07-01", 
    "description": "In this paper we restudy, by a radically different approach, the optimal quadratic cost problem for an abstract dynamics, which models a special class of second-order partial differential equations subject to high internal damping and acted upon by boundary control. A theory for this problem was recently derived in [LLP] and [T1] (see also [T2]) by a change of variable method and by a direct approach, respectively. Unlike [LLP] and [T1], the approach of the present paper is based on singular control theory, combined with regularity theory of the optimal pair from [T1]. This way, not only do we rederive the basic control-theoretic results of [LLP] and [T1]\u2014the (first) synthesis of the optimal pair, and the (first) nonstandard algebraic Riccati equation for the (unique) Riccati operator which enters into the gain operator of the synthesis\u2014but in addition, this method also yields new results\u2014a second form of the synthesis of the optimal pair, and a second (still nonstandard) algebraic Riccati equation for the (still unique) Riccati operator of the synthesis. These results, which show new pathologies in the solution of the problem, are new even in the finite-dimensional case.", 
    "genre": "research_article", 
    "id": "sg:pub.10.1007/bf02683338", 
    "inLanguage": [
      "en"
    ], 
    "isAccessibleForFree": false, 
    "isPartOf": [
      {
        "id": "sg:journal.1120592", 
        "issn": [
          "0095-4616", 
          "1432-0606"
        ], 
        "name": "Applied Mathematics & Optimization", 
        "type": "Periodical"
      }, 
      {
        "issueNumber": "1", 
        "type": "PublicationIssue"
      }, 
      {
        "type": "PublicationVolume", 
        "volumeNumber": "36"
      }
    ], 
    "name": "A singular control approach to highly damped second-order abstract equations and applications", 
    "pagination": "67-107", 
    "productId": [
      {
        "name": "readcube_id", 
        "type": "PropertyValue", 
        "value": [
          "8d746b9dd30478506a4339359bb2c3d7678c21f46257094b4836c3f95d410f4d"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/bf02683338"
        ]
      }, 
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1029693830"
        ]
      }
    ], 
    "sameAs": [
      "https://doi.org/10.1007/bf02683338", 
      "https://app.dimensions.ai/details/publication/pub.1029693830"
    ], 
    "sdDataset": "articles", 
    "sdDatePublished": "2019-04-11T13:29", 
    "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
    "sdPublisher": {
      "name": "Springer Nature - SN SciGraph project", 
      "type": "Organization"
    }, 
    "sdSource": "s3://com-uberresearch-data-dimensions-target-20181106-alternative/cleanup/v134/2549eaecd7973599484d7c17b260dba0a4ecb94b/merge/v9/a6c9fde33151104705d4d7ff012ea9563521a3ce/jats-lookup/v90/0000000370_0000000370/records_46747_00000001.jsonl", 
    "type": "ScholarlyArticle", 
    "url": "http://link.springer.com/10.1007%2FBF02683338"
  }
]
 

Download the RDF metadata as:  json-ld nt turtle xml License info

HOW TO GET THIS DATA PROGRAMMATICALLY:

JSON-LD is a popular format for linked data which is fully compatible with JSON.

curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1007/bf02683338'

N-Triples is a line-based linked data format ideal for batch operations.

curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/bf02683338'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/bf02683338'

RDF/XML is a standard XML format for linked data.

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/bf02683338'


 

This table displays all metadata directly associated to this object as RDF triples.

117 TRIPLES      21 PREDICATES      38 URIs      19 LITERALS      7 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/bf02683338 schema:about anzsrc-for:01
2 anzsrc-for:0101
3 schema:author Nc73d632de3cb4cbbb77b0b4a66e6c4a1
4 schema:citation sg:pub.10.1007/978-1-4612-5561-1
5 sg:pub.10.1007/bf01182784
6 sg:pub.10.1007/bf01442189
7 sg:pub.10.1007/bf01776850
8 sg:pub.10.1007/bf02191985
9 sg:pub.10.1007/bfb0006880
10 https://doi.org/10.1016/0022-247x(70)90283-0
11 https://doi.org/10.1137/0321003
12 https://doi.org/10.1137/0325035
13 https://doi.org/10.1137/0330058
14 https://doi.org/10.1137/0523022
15 schema:datePublished 1997-07
16 schema:datePublishedReg 1997-07-01
17 schema:description In this paper we restudy, by a radically different approach, the optimal quadratic cost problem for an abstract dynamics, which models a special class of second-order partial differential equations subject to high internal damping and acted upon by boundary control. A theory for this problem was recently derived in [LLP] and [T1] (see also [T2]) by a change of variable method and by a direct approach, respectively. Unlike [LLP] and [T1], the approach of the present paper is based on singular control theory, combined with regularity theory of the optimal pair from [T1]. This way, not only do we rederive the basic control-theoretic results of [LLP] and [T1]—the (first) synthesis of the optimal pair, and the (first) nonstandard algebraic Riccati equation for the (unique) Riccati operator which enters into the gain operator of the synthesis—but in addition, this method also yields new results—a second form of the synthesis of the optimal pair, and a second (still nonstandard) algebraic Riccati equation for the (still unique) Riccati operator of the synthesis. These results, which show new pathologies in the solution of the problem, are new even in the finite-dimensional case.
18 schema:genre research_article
19 schema:inLanguage en
20 schema:isAccessibleForFree false
21 schema:isPartOf N617d551058824af498b1581e7c29ec13
22 N74bad8ceee874fc787e31136ea9194b5
23 sg:journal.1120592
24 schema:name A singular control approach to highly damped second-order abstract equations and applications
25 schema:pagination 67-107
26 schema:productId N7f6ba7b2c79f4c5294fcdf51273c4fc7
27 Nc21e590a40af46a995a05124c2d02b4e
28 Ndc7bd0ab0c364e4ea1b93133ae4eb6ef
29 schema:sameAs https://app.dimensions.ai/details/publication/pub.1029693830
30 https://doi.org/10.1007/bf02683338
31 schema:sdDatePublished 2019-04-11T13:29
32 schema:sdLicense https://scigraph.springernature.com/explorer/license/
33 schema:sdPublisher N0dbb0d21fdf448728cf28dcb47410f0a
34 schema:url http://link.springer.com/10.1007%2FBF02683338
35 sgo:license sg:explorer/license/
36 sgo:sdDataset articles
37 rdf:type schema:ScholarlyArticle
38 N0dbb0d21fdf448728cf28dcb47410f0a schema:name Springer Nature - SN SciGraph project
39 rdf:type schema:Organization
40 N28d957a349df4774a5e4cffbf07e1b82 rdf:first sg:person.012351424331.97
41 rdf:rest Nda185ab9a5bb46f78718ab1ae16e61e7
42 N617d551058824af498b1581e7c29ec13 schema:volumeNumber 36
43 rdf:type schema:PublicationVolume
44 N74bad8ceee874fc787e31136ea9194b5 schema:issueNumber 1
45 rdf:type schema:PublicationIssue
46 N7f6ba7b2c79f4c5294fcdf51273c4fc7 schema:name readcube_id
47 schema:value 8d746b9dd30478506a4339359bb2c3d7678c21f46257094b4836c3f95d410f4d
48 rdf:type schema:PropertyValue
49 Nc21e590a40af46a995a05124c2d02b4e schema:name dimensions_id
50 schema:value pub.1029693830
51 rdf:type schema:PropertyValue
52 Nc73d632de3cb4cbbb77b0b4a66e6c4a1 rdf:first sg:person.011122656703.80
53 rdf:rest N28d957a349df4774a5e4cffbf07e1b82
54 Nda185ab9a5bb46f78718ab1ae16e61e7 rdf:first sg:person.01303304750.12
55 rdf:rest rdf:nil
56 Ndc7bd0ab0c364e4ea1b93133ae4eb6ef schema:name doi
57 schema:value 10.1007/bf02683338
58 rdf:type schema:PropertyValue
59 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
60 schema:name Mathematical Sciences
61 rdf:type schema:DefinedTerm
62 anzsrc-for:0101 schema:inDefinedTermSet anzsrc-for:
63 schema:name Pure Mathematics
64 rdf:type schema:DefinedTerm
65 sg:journal.1120592 schema:issn 0095-4616
66 1432-0606
67 schema:name Applied Mathematics & Optimization
68 rdf:type schema:Periodical
69 sg:person.011122656703.80 schema:affiliation https://www.grid.ac/institutes/grid.27755.32
70 schema:familyName Lasiecka
71 schema:givenName I.
72 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.011122656703.80
73 rdf:type schema:Person
74 sg:person.012351424331.97 schema:affiliation https://www.grid.ac/institutes/grid.4800.c
75 schema:familyName Pandolfi
76 schema:givenName L.
77 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012351424331.97
78 rdf:type schema:Person
79 sg:person.01303304750.12 schema:affiliation https://www.grid.ac/institutes/grid.27755.32
80 schema:familyName Triggiani
81 schema:givenName R.
82 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01303304750.12
83 rdf:type schema:Person
84 sg:pub.10.1007/978-1-4612-5561-1 schema:sameAs https://app.dimensions.ai/details/publication/pub.1042930842
85 https://doi.org/10.1007/978-1-4612-5561-1
86 rdf:type schema:CreativeWork
87 sg:pub.10.1007/bf01182784 schema:sameAs https://app.dimensions.ai/details/publication/pub.1021021835
88 https://doi.org/10.1007/bf01182784
89 rdf:type schema:CreativeWork
90 sg:pub.10.1007/bf01442189 schema:sameAs https://app.dimensions.ai/details/publication/pub.1030856017
91 https://doi.org/10.1007/bf01442189
92 rdf:type schema:CreativeWork
93 sg:pub.10.1007/bf01776850 schema:sameAs https://app.dimensions.ai/details/publication/pub.1031864845
94 https://doi.org/10.1007/bf01776850
95 rdf:type schema:CreativeWork
96 sg:pub.10.1007/bf02191985 schema:sameAs https://app.dimensions.ai/details/publication/pub.1037971054
97 https://doi.org/10.1007/bf02191985
98 rdf:type schema:CreativeWork
99 sg:pub.10.1007/bfb0006880 schema:sameAs https://app.dimensions.ai/details/publication/pub.1109719076
100 https://doi.org/10.1007/bfb0006880
101 rdf:type schema:CreativeWork
102 https://doi.org/10.1016/0022-247x(70)90283-0 schema:sameAs https://app.dimensions.ai/details/publication/pub.1010506843
103 rdf:type schema:CreativeWork
104 https://doi.org/10.1137/0321003 schema:sameAs https://app.dimensions.ai/details/publication/pub.1062843669
105 rdf:type schema:CreativeWork
106 https://doi.org/10.1137/0325035 schema:sameAs https://app.dimensions.ai/details/publication/pub.1062843959
107 rdf:type schema:CreativeWork
108 https://doi.org/10.1137/0330058 schema:sameAs https://app.dimensions.ai/details/publication/pub.1062844386
109 rdf:type schema:CreativeWork
110 https://doi.org/10.1137/0523022 schema:sameAs https://app.dimensions.ai/details/publication/pub.1062848435
111 rdf:type schema:CreativeWork
112 https://www.grid.ac/institutes/grid.27755.32 schema:alternateName University of Virginia
113 schema:name Department of Applied Mathematics, Thornton Hall, University of Virginia, 22903, Charlottesville, VA, USA
114 rdf:type schema:Organization
115 https://www.grid.ac/institutes/grid.4800.c schema:alternateName Polytechnic University of Turin
116 schema:name Dipartimento di Matematica, Politecnico di Torino, Corso Duca degli Abruzzi, 24, 10129, Torino, Italy
117 rdf:type schema:Organization
 




Preview window. Press ESC to close (or click here)


...