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A greedy Galerkin method to efficiently select sensors for linear dynamical systems

Journal Article · · Linear Algebra and Its Applications
 [1];  [2];  [3]
  1. Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)
  2. Cornell Univ., Ithaca, NY (United States)
  3. Stanford Univ., CA (United States)
+ Show Author Affiliations

A key challenge in inverse problems is the selection of sensors to gather the most effective data. In this paper, we consider the problem of inferring the initial condition to a linear dynamical system and develop an efficient control-theoretical approach for greedily selecting sensors. Our method employs a Galerkin projection to reduce the size of the inverse problem, resulting in a computationally efficient algorithm for sensor selection. As a byproduct of our algorithm, we obtain a preconditioner for the inverse problem that enables the rapid recovery of the initial condition. Here, we analyze the theoretical performance of our greedy sensor selection algorithm as well as the performance of the associated preconditioner. Finally, we verify our theoretical results on various inverse problems involving partial differential equations.

Research Organization:
Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)
Sponsoring Organization:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); USDOE Laboratory Directed Research and Development (LDRD) Program; US Air Force Office of Scientific Research (AFOSR); National Science Foundation (NSF)
Grant/Contract Number:
NA0003525
OSTI ID:
2311282
Report Number(s):
SAND--2023-10184J
Journal Information:
Linear Algebra and Its Applications, Journal Name: Linear Algebra and Its Applications Vol. 679; ISSN 0024-3795
Publisher:
ElsevierCopyright Statement
Country of Publication:
United States
Language:
English

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Figures / Tables (5)

Algorithm 1(p. 21)figure Algorithm 1
Table 1(p. 23)table Table 1
Figure 1(p. 25)figure Figure 1
Figure 2(p. 26)figure Figure 2
Table 2(p. 27)table Table 2

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Related Subjects

97 MATHEMATICS AND COMPUTING
Galerkin method
Gramian
Greedy algorithm
Inverse problems
Linear dynamics
Lyapunov equation
Observability
Optimal control
Preconditioning
Sensor placement
Submodularity