Resilient Sensor Placement for Kalman Filtering in Networked Systems: Complexity and Algorithms

Given a linear dynamical system affected by noise, we study the problem of optimally placing sensors (at design time) subject to a sensor placement budget constraint in order to minimize the trace of the steady-state error covariance of the corresponding Kalman filter. While this problem is NP-hard...

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Bibliographic Details
Published in:IEEE transactions on control of network systems Vol. 7; no. 4; pp. 1870 - 1881
Main Authors: Ye, Lintao, Roy, Sandip, Sundaram, Shreyas
Format: Journal Article
Language:English
Published: Piscataway IEEE 01.12.2020
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithms
Budgets
Computation
Control systems
Covariance
Directed graphs
Heuristic algorithms
Kalman filters
networked control systems
Optimization
Placement
Polynomials
sensor systems
Sensors
state estimation
Steady state
Stochastic processes
Strategy
System dynamics
ISSN:2325-5870, 2372-2533
Online Access:Get full text
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Summary:Given a linear dynamical system affected by noise, we study the problem of optimally placing sensors (at design time) subject to a sensor placement budget constraint in order to minimize the trace of the steady-state error covariance of the corresponding Kalman filter. While this problem is NP-hard in general, we consider the underlying graph associated with the system dynamics matrix, and focus on the case when there is a single input at one of the nodes in the graph. We provide an optimal strategy (computed in polynomial time) to place the sensors over the network. Next, we consider the problem of attacking (i.e., removing) the placed sensors under a sensor attack budget constraint in order to maximize the trace of the steady-state error covariance of the resulting Kalman filter. Using the insights obtained for the sensor placement problem, we provide an optimal strategy (computed in polynomial time) to attack the placed sensors. Finally, we consider the scenario where a system designer places the sensors under a sensor placement budget constraint, and an adversary then attacks the placed sensors subject to a sensor attack budget constraint. The resilient sensor placement problem is to find a sensor placement strategy to minimize the trace of the steady-state error covariance of the Kalman filter corresponding to the sensors that survive the attack. We show that this problem is NP-hard, and provide a pseudopolynomial-time algorithm to solve it.
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ISSN:2325-5870
2372-2533
DOI:10.1109/TCNS.2020.3006271