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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Vydané v:	IEEE transactions on control of network systems Ročník 7; číslo 4; s. 1870 - 1881
Hlavní autori:	Ye, Lintao, Roy, Sandip, Sundaram, Shreyas
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Piscataway IEEE 01.12.2020 The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Predmet:	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
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Abstract	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.
AbstractList	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.
Author	Roy, Sandip Sundaram, Shreyas Ye, Lintao
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SubjectTerms	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
Title	Resilient Sensor Placement for Kalman Filtering in Networked Systems: Complexity and Algorithms
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