Operator Approach to Linear Control Systems:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht
Springer Netherlands
1996
|
| Schriftenreihe: | Mathematics and Its Applications
345 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | The idea of optimization runs through most parts of control theory. The simplest optimal controls are preplanned (programmed) ones. The problem of constructing optimal preplanned controls has been extensively worked out in literature (see, e. g. , the Pontrjagin maximum principle giving necessary conditions of preplanned control optimality). However, the concept of op timality itself has a restrictive character: it is limited by what one means under optimality in each separate case. The internal contradictoriness of the preplanned control optimality ("the better is the enemy of the good") yields that the practical significance of optimal preplanned controls proves to be not great: such controls are usually sensitive to unregistered disturbances (includ ing the round-off errors which are inevitable when computer devices are used for forming controls), as there is the effect of disturbance accumulation in the control process which makes controls to be of little use on large time inter vals. This gap is mainly provoked by oversimplified settings of optimization problems. The outstanding result of control theory established in the end of the first half of our century is that controls in feedback form ensure the weak sensitivity of closed loop systems with respect to "small" unregistered internal and external disturbances acting in them (here we do not need to discuss performance indexes, since the considered phenomenon is of general nature). But by far not all optimal preplanned controls can be represented in a feedback form |
| Beschreibung: | 1 Online-Ressource (XVI, 398 p) |
| ISBN: | 9789400901278 9789401065443 |
| DOI: | 10.1007/978-94-009-0127-8 |
Internformat
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| 500 | |a The idea of optimization runs through most parts of control theory. The simplest optimal controls are preplanned (programmed) ones. The problem of constructing optimal preplanned controls has been extensively worked out in literature (see, e. g. , the Pontrjagin maximum principle giving necessary conditions of preplanned control optimality). However, the concept of op timality itself has a restrictive character: it is limited by what one means under optimality in each separate case. The internal contradictoriness of the preplanned control optimality ("the better is the enemy of the good") yields that the practical significance of optimal preplanned controls proves to be not great: such controls are usually sensitive to unregistered disturbances (includ ing the round-off errors which are inevitable when computer devices are used for forming controls), as there is the effect of disturbance accumulation in the control process which makes controls to be of little use on large time inter vals. This gap is mainly provoked by oversimplified settings of optimization problems. The outstanding result of control theory established in the end of the first half of our century is that controls in feedback form ensure the weak sensitivity of closed loop systems with respect to "small" unregistered internal and external disturbances acting in them (here we do not need to discuss performance indexes, since the considered phenomenon is of general nature). But by far not all optimal preplanned controls can be represented in a feedback form | ||
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Datensatz im Suchindex
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| author | Cheremensky, A. |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
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| discipline | Mathematik |
| doi_str_mv | 10.1007/978-94-009-0127-8 |
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| isbn | 9789400901278 9789401065443 |
| language | English |
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| spelling | Cheremensky, A. Verfasser aut Operator Approach to Linear Control Systems by A. Cheremensky, V. Fomin Dordrecht Springer Netherlands 1996 1 Online-Ressource (XVI, 398 p) txt rdacontent c rdamedia cr rdacarrier Mathematics and Its Applications 345 The idea of optimization runs through most parts of control theory. The simplest optimal controls are preplanned (programmed) ones. The problem of constructing optimal preplanned controls has been extensively worked out in literature (see, e. g. , the Pontrjagin maximum principle giving necessary conditions of preplanned control optimality). However, the concept of op timality itself has a restrictive character: it is limited by what one means under optimality in each separate case. The internal contradictoriness of the preplanned control optimality ("the better is the enemy of the good") yields that the practical significance of optimal preplanned controls proves to be not great: such controls are usually sensitive to unregistered disturbances (includ ing the round-off errors which are inevitable when computer devices are used for forming controls), as there is the effect of disturbance accumulation in the control process which makes controls to be of little use on large time inter vals. This gap is mainly provoked by oversimplified settings of optimization problems. The outstanding result of control theory established in the end of the first half of our century is that controls in feedback form ensure the weak sensitivity of closed loop systems with respect to "small" unregistered internal and external disturbances acting in them (here we do not need to discuss performance indexes, since the considered phenomenon is of general nature). But by far not all optimal preplanned controls can be represented in a feedback form Mathematics Operator theory Systems theory Mechanical engineering Computer engineering Systems Theory, Control Operator Theory Electrical Engineering Mechanical Engineering Mathematik Operatortheorie (DE-588)4075665-8 gnd rswk-swf Lineares Regelungssystem (DE-588)4167730-4 gnd rswk-swf Lineares Regelungssystem (DE-588)4167730-4 s Operatortheorie (DE-588)4075665-8 s 1\p DE-604 Fomin, V. Sonstige oth https://doi.org/10.1007/978-94-009-0127-8 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Cheremensky, A. Operator Approach to Linear Control Systems Mathematics Operator theory Systems theory Mechanical engineering Computer engineering Systems Theory, Control Operator Theory Electrical Engineering Mechanical Engineering Mathematik Operatortheorie (DE-588)4075665-8 gnd Lineares Regelungssystem (DE-588)4167730-4 gnd |
| subject_GND | (DE-588)4075665-8 (DE-588)4167730-4 |
| title | Operator Approach to Linear Control Systems |
| title_auth | Operator Approach to Linear Control Systems |
| title_exact_search | Operator Approach to Linear Control Systems |
| title_full | Operator Approach to Linear Control Systems by A. Cheremensky, V. Fomin |
| title_fullStr | Operator Approach to Linear Control Systems by A. Cheremensky, V. Fomin |
| title_full_unstemmed | Operator Approach to Linear Control Systems by A. Cheremensky, V. Fomin |
| title_short | Operator Approach to Linear Control Systems |
| title_sort | operator approach to linear control systems |
| topic | Mathematics Operator theory Systems theory Mechanical engineering Computer engineering Systems Theory, Control Operator Theory Electrical Engineering Mechanical Engineering Mathematik Operatortheorie (DE-588)4075665-8 gnd Lineares Regelungssystem (DE-588)4167730-4 gnd |
| topic_facet | Mathematics Operator theory Systems theory Mechanical engineering Computer engineering Systems Theory, Control Operator Theory Electrical Engineering Mechanical Engineering Mathematik Operatortheorie Lineares Regelungssystem |
| url | https://doi.org/10.1007/978-94-009-0127-8 |
| work_keys_str_mv | AT cheremenskya operatorapproachtolinearcontrolsystems AT fominv operatorapproachtolinearcontrolsystems |