Euler’s Method Applied to the Control of Switched Systems View Full Text


Ontology type: schema:Chapter      Open Access: True


Chapter Info

DATE

2017-08-03

AUTHORS

Laurent Fribourg

ABSTRACT

Hybrid systems are a powerful formalism for modeling and reasoning about cyber-physical systems. They mix the continuous and discrete natures of the evolution of computerized systems. Switched systems are a special kind of hybrid systems, with restricted discrete behaviours: those systems only have finitely many different modes of (continuous) evolution, with isolated switches between modes. Such systems provide a good balance between expressiveness and controllability, and are thus in widespread use in large branches of industry such as power electronics and automotive control. The control law for a switched system defines the way of selecting the modes during the run of the system. Controllability is the problem of (automatically) synthesizing a control law in order to satisfy a desired property, such as safety (maintaining the variables within a given zone) or stabilisation (confinement of the variables in a close neighborhood around an objective point). In order to compute the control of a switched system, we need to compute the solutions of the differential equations governing the modes. Euler’s method is the most basic technique for approximating such solutions. We present here an estimation of the Euler’s method local error, using the notion of “one-sided Lispchitz constant” for modes. This yields a general control synthesis approach which can encompass several features such as bounded disturbance and compositionality. More... »

PAGES

3-21

References to SciGraph publications

Book

TITLE

Formal Modeling and Analysis of Timed Systems

ISBN

978-3-319-65764-6
978-3-319-65765-3

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/978-3-319-65765-3_1

DOI

http://dx.doi.org/10.1007/978-3-319-65765-3_1

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1091024864


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/2008/0102", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Applied 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": "Laboratoire Sp\u00e9cification et V\u00e9rification", 
          "id": "https://www.grid.ac/institutes/grid.464035.0", 
          "name": [
            "LSV, CNRS & ENS Paris-Saclay & INRIA, Cachan, France"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Fribourg", 
        "givenName": "Laurent", 
        "id": "sg:person.07426265157.59", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.07426265157.59"
        ], 
        "type": "Person"
      }
    ], 
    "citation": [
      {
        "id": "sg:pub.10.1007/978-3-540-71493-4_34", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1015979671", 
          "https://doi.org/10.1007/978-3-540-71493-4_34"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s10703-014-0211-2", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1018716400", 
          "https://doi.org/10.1007/s10703-014-0211-2"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bfb0080115", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1023900983", 
          "https://doi.org/10.1007/bfb0080115"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-3-7091-6282-8_13", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1030772089", 
          "https://doi.org/10.1007/978-3-7091-6282-8_13"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-3-7091-6282-8_13", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1030772089", 
          "https://doi.org/10.1007/978-3-7091-6282-8_13"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/3-540-36580-x_5", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1036856620", 
          "https://doi.org/10.1007/3-540-36580-x_5"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/3-540-36580-x_5", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1036856620", 
          "https://doi.org/10.1007/3-540-36580-x_5"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.3182/20120606-3-nl-3011.00022", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1038123753"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/3-540-45873-5_6", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1038273250", 
          "https://doi.org/10.1007/3-540-45873-5_6"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-3-540-31954-2_19", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1047312673", 
          "https://doi.org/10.1007/978-3-540-31954-2_19"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-3-540-31954-2_19", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1047312673", 
          "https://doi.org/10.1007/978-3-540-31954-2_19"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/s0005-1098(99)00113-2", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1052264392"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1109/5.871306", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1061180194"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1137/s0363012995293694", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1062881228"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1109/cdc.2005.1582864", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1093498326"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1109/acc.2010.5530715", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1093844017"
        ], 
        "type": "CreativeWork"
      }
    ], 
    "datePublished": "2017-08-03", 
    "datePublishedReg": "2017-08-03", 
    "description": "Hybrid systems are a powerful formalism for modeling and reasoning about cyber-physical systems. They mix the continuous and discrete natures of the evolution of computerized systems. Switched systems are a special kind of hybrid systems, with restricted discrete behaviours: those systems only have finitely many different modes of (continuous) evolution, with isolated switches between modes. Such systems provide a good balance between expressiveness and controllability, and are thus in widespread use in large branches of industry such as power electronics and automotive control. The control law for a switched system defines the way of selecting the modes during the run of the system. Controllability is the problem of (automatically) synthesizing a control law in order to satisfy a desired property, such as safety (maintaining the variables within a given zone) or stabilisation (confinement of the variables in a close neighborhood around an objective point). In order to compute the control of a switched system, we need to compute the solutions of the differential equations governing the modes. Euler\u2019s method is the most basic technique for approximating such solutions. We present here an estimation of the Euler\u2019s method local error, using the notion of \u201cone-sided Lispchitz constant\u201d for modes. This yields a general control synthesis approach which can encompass several features such as bounded disturbance and compositionality.", 
    "editor": [
      {
        "familyName": "Abate", 
        "givenName": "Alessandro", 
        "type": "Person"
      }, 
      {
        "familyName": "Geeraerts", 
        "givenName": "Gilles", 
        "type": "Person"
      }
    ], 
    "genre": "chapter", 
    "id": "sg:pub.10.1007/978-3-319-65765-3_1", 
    "inLanguage": [
      "en"
    ], 
    "isAccessibleForFree": true, 
    "isPartOf": {
      "isbn": [
        "978-3-319-65764-6", 
        "978-3-319-65765-3"
      ], 
      "name": "Formal Modeling and Analysis of Timed Systems", 
      "type": "Book"
    }, 
    "name": "Euler\u2019s Method Applied to the Control of Switched Systems", 
    "pagination": "3-21", 
    "productId": [
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/978-3-319-65765-3_1"
        ]
      }, 
      {
        "name": "readcube_id", 
        "type": "PropertyValue", 
        "value": [
          "068c39cd14de3017e48445f81b959136d0df05a1cb8161fa8917525431647428"
        ]
      }, 
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1091024864"
        ]
      }
    ], 
    "publisher": {
      "location": "Cham", 
      "name": "Springer International Publishing", 
      "type": "Organisation"
    }, 
    "sameAs": [
      "https://doi.org/10.1007/978-3-319-65765-3_1", 
      "https://app.dimensions.ai/details/publication/pub.1091024864"
    ], 
    "sdDataset": "chapters", 
    "sdDatePublished": "2019-04-16T04:59", 
    "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/v90/0000000325_0000000325/records_100778_00000000.jsonl", 
    "type": "Chapter", 
    "url": "https://link.springer.com/10.1007%2F978-3-319-65765-3_1"
  }
]
 

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.10.1007/978-3-319-65765-3_1'

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

curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/978-3-319-65765-3_1'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/978-3-319-65765-3_1'

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

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/978-3-319-65765-3_1'


 

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

116 TRIPLES      23 PREDICATES      39 URIs      19 LITERALS      8 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/978-3-319-65765-3_1 schema:about anzsrc-for:01
2 anzsrc-for:0102
3 schema:author Nf1631edce6fb4331866bb56a5a19a9a4
4 schema:citation sg:pub.10.1007/3-540-36580-x_5
5 sg:pub.10.1007/3-540-45873-5_6
6 sg:pub.10.1007/978-3-540-31954-2_19
7 sg:pub.10.1007/978-3-540-71493-4_34
8 sg:pub.10.1007/978-3-7091-6282-8_13
9 sg:pub.10.1007/bfb0080115
10 sg:pub.10.1007/s10703-014-0211-2
11 https://doi.org/10.1016/s0005-1098(99)00113-2
12 https://doi.org/10.1109/5.871306
13 https://doi.org/10.1109/acc.2010.5530715
14 https://doi.org/10.1109/cdc.2005.1582864
15 https://doi.org/10.1137/s0363012995293694
16 https://doi.org/10.3182/20120606-3-nl-3011.00022
17 schema:datePublished 2017-08-03
18 schema:datePublishedReg 2017-08-03
19 schema:description Hybrid systems are a powerful formalism for modeling and reasoning about cyber-physical systems. They mix the continuous and discrete natures of the evolution of computerized systems. Switched systems are a special kind of hybrid systems, with restricted discrete behaviours: those systems only have finitely many different modes of (continuous) evolution, with isolated switches between modes. Such systems provide a good balance between expressiveness and controllability, and are thus in widespread use in large branches of industry such as power electronics and automotive control. The control law for a switched system defines the way of selecting the modes during the run of the system. Controllability is the problem of (automatically) synthesizing a control law in order to satisfy a desired property, such as safety (maintaining the variables within a given zone) or stabilisation (confinement of the variables in a close neighborhood around an objective point). In order to compute the control of a switched system, we need to compute the solutions of the differential equations governing the modes. Euler’s method is the most basic technique for approximating such solutions. We present here an estimation of the Euler’s method local error, using the notion of “one-sided Lispchitz constant” for modes. This yields a general control synthesis approach which can encompass several features such as bounded disturbance and compositionality.
20 schema:editor N4f1a79c190d347e198386f149c3d5ac4
21 schema:genre chapter
22 schema:inLanguage en
23 schema:isAccessibleForFree true
24 schema:isPartOf N44d8a793aa844eb3b8805bf30a6e8a3b
25 schema:name Euler’s Method Applied to the Control of Switched Systems
26 schema:pagination 3-21
27 schema:productId Na46b2d1f52644d16939f81261119ae7e
28 Nc8f938f1055343628627edfe370bd6a4
29 Nd698cf8578974edc89898eab3fa1ec7f
30 schema:publisher Nfa86209c6ef94cba884a30d903fd429f
31 schema:sameAs https://app.dimensions.ai/details/publication/pub.1091024864
32 https://doi.org/10.1007/978-3-319-65765-3_1
33 schema:sdDatePublished 2019-04-16T04:59
34 schema:sdLicense https://scigraph.springernature.com/explorer/license/
35 schema:sdPublisher Ne4f36eb101bf4c798ccfa0e44ffe6015
36 schema:url https://link.springer.com/10.1007%2F978-3-319-65765-3_1
37 sgo:license sg:explorer/license/
38 sgo:sdDataset chapters
39 rdf:type schema:Chapter
40 N1a789e3a4386490c9c4f72f24373ccf7 schema:familyName Geeraerts
41 schema:givenName Gilles
42 rdf:type schema:Person
43 N1a80f17054a144a98a5c19d0a2bffa55 schema:familyName Abate
44 schema:givenName Alessandro
45 rdf:type schema:Person
46 N44d8a793aa844eb3b8805bf30a6e8a3b schema:isbn 978-3-319-65764-6
47 978-3-319-65765-3
48 schema:name Formal Modeling and Analysis of Timed Systems
49 rdf:type schema:Book
50 N4f1a79c190d347e198386f149c3d5ac4 rdf:first N1a80f17054a144a98a5c19d0a2bffa55
51 rdf:rest N75537baeb4b14177a4be4d078df824bd
52 N75537baeb4b14177a4be4d078df824bd rdf:first N1a789e3a4386490c9c4f72f24373ccf7
53 rdf:rest rdf:nil
54 Na46b2d1f52644d16939f81261119ae7e schema:name readcube_id
55 schema:value 068c39cd14de3017e48445f81b959136d0df05a1cb8161fa8917525431647428
56 rdf:type schema:PropertyValue
57 Nc8f938f1055343628627edfe370bd6a4 schema:name doi
58 schema:value 10.1007/978-3-319-65765-3_1
59 rdf:type schema:PropertyValue
60 Nd698cf8578974edc89898eab3fa1ec7f schema:name dimensions_id
61 schema:value pub.1091024864
62 rdf:type schema:PropertyValue
63 Ne4f36eb101bf4c798ccfa0e44ffe6015 schema:name Springer Nature - SN SciGraph project
64 rdf:type schema:Organization
65 Nf1631edce6fb4331866bb56a5a19a9a4 rdf:first sg:person.07426265157.59
66 rdf:rest rdf:nil
67 Nfa86209c6ef94cba884a30d903fd429f schema:location Cham
68 schema:name Springer International Publishing
69 rdf:type schema:Organisation
70 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
71 schema:name Mathematical Sciences
72 rdf:type schema:DefinedTerm
73 anzsrc-for:0102 schema:inDefinedTermSet anzsrc-for:
74 schema:name Applied Mathematics
75 rdf:type schema:DefinedTerm
76 sg:person.07426265157.59 schema:affiliation https://www.grid.ac/institutes/grid.464035.0
77 schema:familyName Fribourg
78 schema:givenName Laurent
79 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.07426265157.59
80 rdf:type schema:Person
81 sg:pub.10.1007/3-540-36580-x_5 schema:sameAs https://app.dimensions.ai/details/publication/pub.1036856620
82 https://doi.org/10.1007/3-540-36580-x_5
83 rdf:type schema:CreativeWork
84 sg:pub.10.1007/3-540-45873-5_6 schema:sameAs https://app.dimensions.ai/details/publication/pub.1038273250
85 https://doi.org/10.1007/3-540-45873-5_6
86 rdf:type schema:CreativeWork
87 sg:pub.10.1007/978-3-540-31954-2_19 schema:sameAs https://app.dimensions.ai/details/publication/pub.1047312673
88 https://doi.org/10.1007/978-3-540-31954-2_19
89 rdf:type schema:CreativeWork
90 sg:pub.10.1007/978-3-540-71493-4_34 schema:sameAs https://app.dimensions.ai/details/publication/pub.1015979671
91 https://doi.org/10.1007/978-3-540-71493-4_34
92 rdf:type schema:CreativeWork
93 sg:pub.10.1007/978-3-7091-6282-8_13 schema:sameAs https://app.dimensions.ai/details/publication/pub.1030772089
94 https://doi.org/10.1007/978-3-7091-6282-8_13
95 rdf:type schema:CreativeWork
96 sg:pub.10.1007/bfb0080115 schema:sameAs https://app.dimensions.ai/details/publication/pub.1023900983
97 https://doi.org/10.1007/bfb0080115
98 rdf:type schema:CreativeWork
99 sg:pub.10.1007/s10703-014-0211-2 schema:sameAs https://app.dimensions.ai/details/publication/pub.1018716400
100 https://doi.org/10.1007/s10703-014-0211-2
101 rdf:type schema:CreativeWork
102 https://doi.org/10.1016/s0005-1098(99)00113-2 schema:sameAs https://app.dimensions.ai/details/publication/pub.1052264392
103 rdf:type schema:CreativeWork
104 https://doi.org/10.1109/5.871306 schema:sameAs https://app.dimensions.ai/details/publication/pub.1061180194
105 rdf:type schema:CreativeWork
106 https://doi.org/10.1109/acc.2010.5530715 schema:sameAs https://app.dimensions.ai/details/publication/pub.1093844017
107 rdf:type schema:CreativeWork
108 https://doi.org/10.1109/cdc.2005.1582864 schema:sameAs https://app.dimensions.ai/details/publication/pub.1093498326
109 rdf:type schema:CreativeWork
110 https://doi.org/10.1137/s0363012995293694 schema:sameAs https://app.dimensions.ai/details/publication/pub.1062881228
111 rdf:type schema:CreativeWork
112 https://doi.org/10.3182/20120606-3-nl-3011.00022 schema:sameAs https://app.dimensions.ai/details/publication/pub.1038123753
113 rdf:type schema:CreativeWork
114 https://www.grid.ac/institutes/grid.464035.0 schema:alternateName Laboratoire Spécification et Vérification
115 schema:name LSV, CNRS & ENS Paris-Saclay & INRIA, Cachan, France
116 rdf:type schema:Organization
 




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


...