Time-Delayed Linear Quadratic Optimal Control Problems
This book characterizes the open-loop and closed-loop solvability for time-delayed linear quadratic optimal control problems. Different from the existing literature, in the current book, we present a theory of deterministic LQ problems with delays which has several new features: Our system is time-v...
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| Médium: | Elektronický zdroj E-kniha |
| Jazyk: | angličtina |
| Vydáno: |
Singapore :
Springer Nature Singapore : Imprint: Springer,
2025.
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| Vydání: | 1st ed. 2025. |
| Edice: | SpringerBriefs on PDEs and Data Science,
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| On-line přístup: | https://doi.org/10.1007/978-981-96-1897-2 |
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| 100 | 1 | |a Meng, Weijun. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 245 | 1 | 0 | |a Time-Delayed Linear Quadratic Optimal Control Problems |h [electronic resource] / |c by Weijun Meng, Jingtao Shi, Jiongmin Yong. |
| 250 | |a 1st ed. 2025. | ||
| 264 | 1 | |a Singapore : |b Springer Nature Singapore : |b Imprint: Springer, |c 2025. | |
| 300 | |a 1 online resource (XI, 150 p. 3 illus.). |b 2 illus. in color. | ||
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| 341 | 0 | |b Single logical reading order |2 onix | |
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| 505 | 0 | |a Chapter 1 Introduction -- Chapter 2 Problem Lifting -- Chapter 3 Solutions to the LQ Problems. | |
| 520 | |a This book characterizes the open-loop and closed-loop solvability for time-delayed linear quadratic optimal control problems. Different from the existing literature, in the current book, we present a theory of deterministic LQ problems with delays which has several new features: Our system is time-varying, with both the state equation and cost functional being allowed to include discrete and distributed delays, both in the state and the control. We take different approaches to discuss the unboundedness of the control operator. The open-loop solvability of the lifted problem is characterized by the solvability of a system of forward-backward integral evolution equations and the convexity condition of the cost functional. Surprisingly, the adjoint equations involve some coupled partial differential equations, which is significantly different from that in the literature, where, the adjoint equations are all some anticipated backward ordinary differential equations. The closed-loop solvability is characterized by the solvability of three equivalent integral operator-valued Riccati equations and two equivalent backward integral evolution equations which are much easier to handle than the differential operator-valued Riccati equations used in the literature to study similar problems. The closed-loop representation of open-loop optimal control is presented through three equivalent integral operator-valued Riccati equations. | ||
| 532 | 8 | |a Accessibility summary: This PDF does Not fully comply with PDF/UA standards but does include limited screen reader support, descriptions for Non-text content (such as images and graphs), bookmarks for easy navigation, and searchable, selectable text. Users of assistive technologies may experience difficulty navigating or interpreting content in this document. We recognise the importance of accessibility and welcome queries about accessibility for any of our products. If you have a question or an access need, please get in touch with us via https://www.springernature.com/gp/info/accessibility | |
| 532 | 8 | |a Inaccessible, or known limited accessibility | |
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| 532 | 8 | |a Publisher contact for further accessibility information: accessibilitysupport@springernature.com | |
| 588 | |a Print version record. | ||
| 650 | 0 | |a System theory. | |
| 650 | 0 | |a Control theory. | |
| 650 | 0 | |a Mathematical optimization. | |
| 650 | 1 | 4 | |a Systems Theory, Control. |
| 650 | 2 | 4 | |a Optimization. |
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| 700 | 1 | |a Yong, Jiongmin. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
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