Differential and algebraic Riccati equations with application to boundary point control problems: continuous theory and approximation theory
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin u.a.
Springer
1991
|
| Schriftenreihe: | Lecture notes in control and information sciences
164 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XI, 160 S. |
| ISBN: | 3540543392 0387543392 |
Internformat
MARC
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| 100 | 1 | |a Lasiecka, Irena |d 1948- |e Verfasser |0 (DE-588)111374383 |4 aut | |
| 245 | 1 | 0 | |a Differential and algebraic Riccati equations with application to boundary point control problems |b continuous theory and approximation theory |c I. Lasiecka ; R. Triggiani |
| 264 | 1 | |a Berlin u.a. |b Springer |c 1991 | |
| 300 | |a XI, 160 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Lecture notes in control and information sciences |v 164 | |
| 650 | 7 | |a Commande, théorie de la |2 ram | |
| 650 | 7 | |a Optimisation mathématique |2 ram | |
| 650 | 7 | |a Riccati, équation de |2 ram | |
| 650 | 4 | |a Control theory | |
| 650 | 4 | |a Mathematical optimization | |
| 650 | 4 | |a Riccati equation | |
| 650 | 0 | 7 | |a Randwertproblem |0 (DE-588)4048395-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Lineares dynamisches System |0 (DE-588)4167727-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Riccati-Differentialgleichung |0 (DE-588)4230752-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Optimale Kontrolle |0 (DE-588)4121428-6 |2 gnd |9 rswk-swf |
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| 689 | 0 | 2 | |a Riccati-Differentialgleichung |0 (DE-588)4230752-1 |D s |
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| 689 | 1 | 2 | |a Riccati-Differentialgleichung |0 (DE-588)4230752-1 |D s |
| 689 | 1 | |5 DE-604 | |
| 700 | 1 | |a Triggiani, Roberto |d 1942- |e Verfasser |0 (DE-588)112914292 |4 aut | |
| 830 | 0 | |a Lecture notes in control and information sciences |v 164 |w (DE-604)BV005848579 |9 164 | |
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Datensatz im Suchindex
| _version_ | 1805082716655321088 |
|---|---|
| adam_text |
Table of Contents
1. Introduction; two abstract classes; statement of main
problems 1
PART I: Continuous theory. Case T «°
2. Abstract Differential Riccati Equation for the first class
subject to the analyticity assumption (H.I) = (1.5) 8
2.1. The general case 8
2.2. The smoothing case 12
2.3. Counterexamples 17
3. Abstract Differential Riccati Equation for the second class
subject to the trace regularity assumption (H.2) (1.6) . . 22
3.1. Pointwise synthesis of optimal pair 22
3.2. The DRE for second order hyperbolic equations
with Dirichlet control: existence and properties . 24
3.3. The DRE: existence and uniqueness 26
3.4. Nonsmoothing case: weaker notions of solution 28
4. Abstract Differential Riccati Equation for the second class
subject to the regularity assumption (H.2,,) = (1.8) 31
4.1. Theoretical results: Theorems 4.1 and 4.2 32
Case T = «•
5. Abstract Algebraic Riccati Equations: Existence and
uniqueness 35
5.1. Algebraic Riccati Equation for the first class subject
to the analyticity assumption (H.I) = (1.5) 36
5.2. Algebraic Riccati Equation for the second class subject
to the trace regularity assumption (H.2) = (1.6) . 39
6. Examples of partial differential equation problems
satisfying (H.I) 51
6.1. Class (H.I): Heat equation with Dirichlet boundary
control 51
6.2. Class (H.I): Heat equation with Neumann boundary
control 53
6.3. Class (H.I): Structurally damped plates with point
control or boundary control 57
7. Examples of partial differential equation problems
satisfying (H.2) 71
X
7.1. Class (H.2): Second order hyperbolic equations with
Dirichlet boundary control 71
7.2. Class (H.2): Euler Bernoulli equations with boundary
control 75
7.3. Class (H.2): Schrodinger equation with Dirichlet
boundary control 83
7.4. Class (H.2): First order hyperbolic systems 85
7.5. TJlass (H.2): Kirchoff plate with boundary control in
the bending moment 88
7.6. Class (H.2): A two dimensional plate model with
boundary control as a bending moment 91
7.7. Class (H.2): Wave equation with interior point
control 94
7.8. Class (H.2): Kirchhoff equation with interior
point control 97
8. Example of a partial differential equation problem
satisfying (H.2D) 101
8.1. Boundary control/boundary observation for hyperbolic
mixed problems of Neumann type. Application of
Theorems 4.1 and 4.2 101
PART II: Approximation theory
9. Numerical approximation of the solution to the abstract
Algebraic Riccati Equation 107
9.1. Approximation for the (H.I) class 110
9.1.1. Approximation assumptions 110
9.1.2. Consequences of approximating assumptions
on A and B Ill
9.1.3. Approximation of dynamics and of control
problems. Related Riccati Equation 112
9.1.4. Main results of approximating schemes 113
9.2. Approximation for the (H.2) class 121
9.2.1. Approximating assumptions 121
9.2.2. Approximation of dynamics and of control
problems. Related Riccati Equation 122
9.2.3. Approximating results 122
9.2.4. Discussion on the assumptions 125
9.2.5. Literature 126
XI
10. Examples of numerical approximation for the classes (H.I)
and (H.2) 126
10.1. Class (H.I): Heat equation with Dirichlet boundary
control 126
10.2. Class (H.I): The structurally damped plate problem in
Example 3.1 134
10.3. Class (H.2): The wave equation with Dirichlet boundary
control 138
10.4. Class (H.2): First order hyperbolic systems 145
11. Conclusions 149
11.1. Theoretical aspects 149
11.2. Numerical aspects 150 |
| any_adam_object | 1 |
| author | Lasiecka, Irena 1948- Triggiani, Roberto 1942- |
| author_GND | (DE-588)111374383 (DE-588)112914292 |
| author_facet | Lasiecka, Irena 1948- Triggiani, Roberto 1942- |
| author_role | aut aut |
| author_sort | Lasiecka, Irena 1948- |
| author_variant | i l il r t rt |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SI 845 SK 540 |
| classification_tum | MAT 496f MAT 342f |
| ctrlnum | (OCoLC)243706541 (DE-599)BVBBV004540205 |
| dewey-full | 515/.352 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
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| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV004540205 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-20T07:37:05Z |
| institution | BVB |
| isbn | 3540543392 0387543392 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002795160 |
| oclc_num | 243706541 |
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| physical | XI, 160 S. |
| publishDate | 1991 |
| publishDateSearch | 1991 |
| publishDateSort | 1991 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in control and information sciences |
| series2 | Lecture notes in control and information sciences |
| spelling | Lasiecka, Irena 1948- Verfasser (DE-588)111374383 aut Differential and algebraic Riccati equations with application to boundary point control problems continuous theory and approximation theory I. Lasiecka ; R. Triggiani Berlin u.a. Springer 1991 XI, 160 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in control and information sciences 164 Commande, théorie de la ram Optimisation mathématique ram Riccati, équation de ram Control theory Mathematical optimization Riccati equation Randwertproblem (DE-588)4048395-2 gnd rswk-swf Lineares dynamisches System (DE-588)4167727-4 gnd rswk-swf Riccati-Differentialgleichung (DE-588)4230752-1 gnd rswk-swf Optimale Kontrolle (DE-588)4121428-6 gnd rswk-swf Lineares dynamisches System (DE-588)4167727-4 s Optimale Kontrolle (DE-588)4121428-6 s Riccati-Differentialgleichung (DE-588)4230752-1 s DE-604 Randwertproblem (DE-588)4048395-2 s Triggiani, Roberto 1942- Verfasser (DE-588)112914292 aut Lecture notes in control and information sciences 164 (DE-604)BV005848579 164 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002795160&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lasiecka, Irena 1948- Triggiani, Roberto 1942- Differential and algebraic Riccati equations with application to boundary point control problems continuous theory and approximation theory Lecture notes in control and information sciences Commande, théorie de la ram Optimisation mathématique ram Riccati, équation de ram Control theory Mathematical optimization Riccati equation Randwertproblem (DE-588)4048395-2 gnd Lineares dynamisches System (DE-588)4167727-4 gnd Riccati-Differentialgleichung (DE-588)4230752-1 gnd Optimale Kontrolle (DE-588)4121428-6 gnd |
| subject_GND | (DE-588)4048395-2 (DE-588)4167727-4 (DE-588)4230752-1 (DE-588)4121428-6 |
| title | Differential and algebraic Riccati equations with application to boundary point control problems continuous theory and approximation theory |
| title_auth | Differential and algebraic Riccati equations with application to boundary point control problems continuous theory and approximation theory |
| title_exact_search | Differential and algebraic Riccati equations with application to boundary point control problems continuous theory and approximation theory |
| title_full | Differential and algebraic Riccati equations with application to boundary point control problems continuous theory and approximation theory I. Lasiecka ; R. Triggiani |
| title_fullStr | Differential and algebraic Riccati equations with application to boundary point control problems continuous theory and approximation theory I. Lasiecka ; R. Triggiani |
| title_full_unstemmed | Differential and algebraic Riccati equations with application to boundary point control problems continuous theory and approximation theory I. Lasiecka ; R. Triggiani |
| title_short | Differential and algebraic Riccati equations with application to boundary point control problems |
| title_sort | differential and algebraic riccati equations with application to boundary point control problems continuous theory and approximation theory |
| title_sub | continuous theory and approximation theory |
| topic | Commande, théorie de la ram Optimisation mathématique ram Riccati, équation de ram Control theory Mathematical optimization Riccati equation Randwertproblem (DE-588)4048395-2 gnd Lineares dynamisches System (DE-588)4167727-4 gnd Riccati-Differentialgleichung (DE-588)4230752-1 gnd Optimale Kontrolle (DE-588)4121428-6 gnd |
| topic_facet | Commande, théorie de la Optimisation mathématique Riccati, équation de Control theory Mathematical optimization Riccati equation Randwertproblem Lineares dynamisches System Riccati-Differentialgleichung Optimale Kontrolle |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002795160&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV005848579 |
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