Min-plus techniques for set-valued state estimation

Abhijit G. Kallapur; Srinivas Sridharan; William M. McEneaney; Ian R. Petersen

doi:10.1109/CDC.2012.6426133

Min-plus techniques for set-valued state estimation

Abhijit G. Kallapur^*, Srinivas Sridharan, William M. McEneaney, Ian R. Petersen

^*Corresponding author for this work

Research output: Contribution to journal › Conference article › peer-review

1 Citation (Scopus)

Abstract

This article approaches the deterministic filtering problem for a discrete-time nonlinear system (nonlinear dynamics and output functions) with a sum quadratic constraint on the process and the measurement disturbances. The problem is formulated using an optimal control framework and the solution to the associated Hamilton-Jacobi-Bellman (HJB) equation is obtained. This approach enables the design of the filter without recourse to linearization of the system dynamics/ output equation and yields a set-valued state estimator. A computationally tractable numerical algorithm is introduced by utilizing the min-plus linearity of the corresponding dynamic programming operator.

Original language	English
Article number	6426133
Pages (from-to)	6009-6014
Number of pages	6
Journal	Proceedings of the IEEE Conference on Decision and Control
DOIs	https://doi.org/10.1109/CDC.2012.6426133
Publication status	Published - 2012
Externally published	Yes
Event	51st IEEE Conference on Decision and Control, CDC 2012 - Maui, HI, United States Duration: 10 Dec 2012 → 13 Dec 2012

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10.1109/CDC.2012.6426133

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title = "Min-plus techniques for set-valued state estimation",

abstract = "This article approaches the deterministic filtering problem for a discrete-time nonlinear system (nonlinear dynamics and output functions) with a sum quadratic constraint on the process and the measurement disturbances. The problem is formulated using an optimal control framework and the solution to the associated Hamilton-Jacobi-Bellman (HJB) equation is obtained. This approach enables the design of the filter without recourse to linearization of the system dynamics/ output equation and yields a set-valued state estimator. A computationally tractable numerical algorithm is introduced by utilizing the min-plus linearity of the corresponding dynamic programming operator.",

author = "Kallapur, {Abhijit G.} and Srinivas Sridharan and McEneaney, {William M.} and Petersen, {Ian R.}",

year = "2012",

doi = "10.1109/CDC.2012.6426133",

language = "English",

pages = "6009--6014",

journal = "Proceedings of the IEEE Conference on Decision and Control",

issn = "0743-1546",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

note = "51st IEEE Conference on Decision and Control, CDC 2012 ; Conference date: 10-12-2012 Through 13-12-2012",

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T1 - Min-plus techniques for set-valued state estimation

AU - Kallapur, Abhijit G.

AU - Sridharan, Srinivas

AU - McEneaney, William M.

AU - Petersen, Ian R.

PY - 2012

Y1 - 2012

N2 - This article approaches the deterministic filtering problem for a discrete-time nonlinear system (nonlinear dynamics and output functions) with a sum quadratic constraint on the process and the measurement disturbances. The problem is formulated using an optimal control framework and the solution to the associated Hamilton-Jacobi-Bellman (HJB) equation is obtained. This approach enables the design of the filter without recourse to linearization of the system dynamics/ output equation and yields a set-valued state estimator. A computationally tractable numerical algorithm is introduced by utilizing the min-plus linearity of the corresponding dynamic programming operator.

AB - This article approaches the deterministic filtering problem for a discrete-time nonlinear system (nonlinear dynamics and output functions) with a sum quadratic constraint on the process and the measurement disturbances. The problem is formulated using an optimal control framework and the solution to the associated Hamilton-Jacobi-Bellman (HJB) equation is obtained. This approach enables the design of the filter without recourse to linearization of the system dynamics/ output equation and yields a set-valued state estimator. A computationally tractable numerical algorithm is introduced by utilizing the min-plus linearity of the corresponding dynamic programming operator.

UR - http://www.scopus.com/inward/record.url?scp=84874243760&partnerID=8YFLogxK

U2 - 10.1109/CDC.2012.6426133

DO - 10.1109/CDC.2012.6426133

M3 - Conference article

AN - SCOPUS:84874243760

SN - 0743-1546

SP - 6009

EP - 6014

JO - Proceedings of the IEEE Conference on Decision and Control

JF - Proceedings of the IEEE Conference on Decision and Control

M1 - 6426133

T2 - 51st IEEE Conference on Decision and Control, CDC 2012

Y2 - 10 December 2012 through 13 December 2012

ER -

Min-plus techniques for set-valued state estimation

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