Discrete‐time linear quadratic gaussian control with input delay and Markovian packet dropouts.
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| Title: | Discrete‐time linear quadratic gaussian control with input delay and Markovian packet dropouts. |
|---|---|
| Authors: | Lu, Xiao1 (AUTHOR), Cai, Yuanyu2 (AUTHOR), Liang, Xiao3 (AUTHOR) liangxiao_sdu@163.com, Sun, Hongyu1 (AUTHOR) |
| Source: | Optimal Control - Applications & Methods. Jul2024, Vol. 45 Issue 4, p1736-1749. 14p. |
| Subjects: | Stochastic difference equations, Mathematical decoupling, Cost functions, Maximum principles (Mathematics), Discrete-time systems, Riccati equation, Linear systems, Stability of linear systems |
| Abstract: | This article investigates the finite horizon linear quadratic gaussian (LQG) control problem for networked control systems with two‐way Markovian packet dropouts and input delay, where packet dropouts occur from the sensor to the estimator and from the controller to the actuator, and delay occurs from the controller to the actuator. The novelty of this work lies in providing a complete solution for the optimal control problem subject to two‐way Markovian packet dropouts and input delay. The contributions of this article are as follows: first, by applying the maximum principle to the discrete‐time linear systems and the quadratic cost function involving input delay and Markovian packet dropouts, a solution to the forward and backward stochastic difference equations (FBSDEs) is derived. Second, a sufficient and necessary condition for the optimal control problem is obtained by decoupling the coupled Riccati equations. Finally, the explicit solution of the optimal controller is presented based on the complete square method. Numerical examples are provided to demonstrate the validity of the theoretical results. [ABSTRACT FROM AUTHOR] |
| Copyright of Optimal Control - Applications & Methods is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
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| Header | DbId: egs DbLabel: Engineering Source An: 178211197 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Discrete‐time linear quadratic gaussian control with input delay and Markovian packet dropouts. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Lu%2C+Xiao%22">Lu, Xiao</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Cai%2C+Yuanyu%22">Cai, Yuanyu</searchLink><relatesTo>2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Liang%2C+Xiao%22">Liang, Xiao</searchLink><relatesTo>3</relatesTo> (AUTHOR)<i> liangxiao_sdu@163.com</i><br /><searchLink fieldCode="AR" term="%22Sun%2C+Hongyu%22">Sun, Hongyu</searchLink><relatesTo>1</relatesTo> (AUTHOR) – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Optimal+Control+-+Applications+%26+Methods%22">Optimal Control - Applications & Methods</searchLink>. Jul2024, Vol. 45 Issue 4, p1736-1749. 14p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Stochastic+difference+equations%22">Stochastic difference equations</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+decoupling%22">Mathematical decoupling</searchLink><br /><searchLink fieldCode="DE" term="%22Cost+functions%22">Cost functions</searchLink><br /><searchLink fieldCode="DE" term="%22Maximum+principles+%28Mathematics%29%22">Maximum principles (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Discrete-time+systems%22">Discrete-time systems</searchLink><br /><searchLink fieldCode="DE" term="%22Riccati+equation%22">Riccati equation</searchLink><br /><searchLink fieldCode="DE" term="%22Linear+systems%22">Linear systems</searchLink><br /><searchLink fieldCode="DE" term="%22Stability+of+linear+systems%22">Stability of linear systems</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: This article investigates the finite horizon linear quadratic gaussian (LQG) control problem for networked control systems with two‐way Markovian packet dropouts and input delay, where packet dropouts occur from the sensor to the estimator and from the controller to the actuator, and delay occurs from the controller to the actuator. The novelty of this work lies in providing a complete solution for the optimal control problem subject to two‐way Markovian packet dropouts and input delay. The contributions of this article are as follows: first, by applying the maximum principle to the discrete‐time linear systems and the quadratic cost function involving input delay and Markovian packet dropouts, a solution to the forward and backward stochastic difference equations (FBSDEs) is derived. Second, a sufficient and necessary condition for the optimal control problem is obtained by decoupling the coupled Riccati equations. Finally, the explicit solution of the optimal controller is presented based on the complete square method. Numerical examples are provided to demonstrate the validity of the theoretical results. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Optimal Control - Applications & Methods is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1002/oca.3119 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 14 StartPage: 1736 Subjects: – SubjectFull: Stochastic difference equations Type: general – SubjectFull: Mathematical decoupling Type: general – SubjectFull: Cost functions Type: general – SubjectFull: Maximum principles (Mathematics) Type: general – SubjectFull: Discrete-time systems Type: general – SubjectFull: Riccati equation Type: general – SubjectFull: Linear systems Type: general – SubjectFull: Stability of linear systems Type: general Titles: – TitleFull: Discrete‐time linear quadratic gaussian control with input delay and Markovian packet dropouts. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Lu, Xiao – PersonEntity: Name: NameFull: Cai, Yuanyu – PersonEntity: Name: NameFull: Liang, Xiao – PersonEntity: Name: NameFull: Sun, Hongyu IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 07 Text: Jul2024 Type: published Y: 2024 Identifiers: – Type: issn-print Value: 01432087 Numbering: – Type: volume Value: 45 – Type: issue Value: 4 Titles: – TitleFull: Optimal Control - Applications & Methods Type: main |
| ResultId | 1 |
