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Optimal estimation and control for lossy network: stability, convergence, and performance

Optimal estimation and control for lossy network: stability, convergence, and performance
Optimal estimation and control for lossy network: stability, convergence, and performance
In this paper, we study the problems of optimal estimation and control, i.e., the linear quadratic Gaussian (LQG) control, for systems with packet losses but without acknowledgment. Such acknowledgment is a signal sent by the actuator to inform the estimator of the incidence of control packet losses. For such system, which is usually called as a user datagram protocol (UDP)-like system, the optimal estimation is nonlinear and its calculation is time-consuming, making its corresponding optimal LQG problem complicated. We first propose two conditions: 1) the sensor has some computation abilities; and 2) the control command, exerted to the plant, is known to the sensor. For a UDP-like system satisfying these two conditions, we derive the optimal estimation. By constructing the finite and infinite product probability measure spaces for the estimation error covariances (EEC), we give the stability condition for the expected EEC, and show the existence of a measurable function to which the EEC converges in distribution, and propose some practical methods to evaluate the estimation performance. Finally, the LQG controllers are derived, and the conditions for the mean square stability of the closed-loop system are established.
0018-9286
4564-4579
Lin, Hong
1c7e2576-2249-4c3c-98ab-b0a3436780cf
Su, Hongye
49abac6c-096f-493e-b412-8948bbea3c30
Shi, Peng
81111e49-129d-45ba-9035-1cb28977bd2a
Shu, Zhan
ea5dc18c-d375-4db0-bbcc-dd0229f3a1cb
Lu, Renquan
39a0cc23-d198-407d-8977-b440787536da
Wu, Zheng-Guang
e1f8329d-5986-4dba-8da4-494572aab81f
Lin, Hong
1c7e2576-2249-4c3c-98ab-b0a3436780cf
Su, Hongye
49abac6c-096f-493e-b412-8948bbea3c30
Shi, Peng
81111e49-129d-45ba-9035-1cb28977bd2a
Shu, Zhan
ea5dc18c-d375-4db0-bbcc-dd0229f3a1cb
Lu, Renquan
39a0cc23-d198-407d-8977-b440787536da
Wu, Zheng-Guang
e1f8329d-5986-4dba-8da4-494572aab81f

Lin, Hong, Su, Hongye, Shi, Peng, Shu, Zhan, Lu, Renquan and Wu, Zheng-Guang (2017) Optimal estimation and control for lossy network: stability, convergence, and performance. IEEE Transactions on Automatic Control, 62 (9), 4564-4579. (doi:10.1109/TAC.2017.2672729).

Record type: Article

Abstract

In this paper, we study the problems of optimal estimation and control, i.e., the linear quadratic Gaussian (LQG) control, for systems with packet losses but without acknowledgment. Such acknowledgment is a signal sent by the actuator to inform the estimator of the incidence of control packet losses. For such system, which is usually called as a user datagram protocol (UDP)-like system, the optimal estimation is nonlinear and its calculation is time-consuming, making its corresponding optimal LQG problem complicated. We first propose two conditions: 1) the sensor has some computation abilities; and 2) the control command, exerted to the plant, is known to the sensor. For a UDP-like system satisfying these two conditions, we derive the optimal estimation. By constructing the finite and infinite product probability measure spaces for the estimation error covariances (EEC), we give the stability condition for the expected EEC, and show the existence of a measurable function to which the EEC converges in distribution, and propose some practical methods to evaluate the estimation performance. Finally, the LQG controllers are derived, and the conditions for the mean square stability of the closed-loop system are established.

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Accepted/In Press date: 2 February 2017
e-pub ahead of print date: 22 February 2017
Organisations: Mechatronics

Identifiers

Local EPrints ID: 405528
URI: http://eprints.soton.ac.uk/id/eprint/405528
ISSN: 0018-9286
PURE UUID: 6601c3a6-dcd2-4ba0-a265-7ceba5abe4b4
ORCID for Zhan Shu: ORCID iD orcid.org/0000-0002-5933-254X

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Date deposited: 07 Feb 2017 11:21
Last modified: 15 Mar 2024 04:31

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Contributors

Author: Hong Lin
Author: Hongye Su
Author: Peng Shi
Author: Zhan Shu ORCID iD
Author: Renquan Lu
Author: Zheng-Guang Wu

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