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Optimal Sensor Selection for Estimation of Distributed Parameter Systems

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Automatic Control, Robotics, and Information Processing

Part of the book series: Studies in Systems, Decision and Control ((SSDC,volume 296))

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Abstract

This chapter is focused on spatial sensor location for maximization of identification accuracy of distributed parameter systems. The following problem formulation, in terms of optimum experimental design, is adopted, in which the optimality criterion is a convex function defined on the Fisher information matrix associated with estimated parameters. The locations of a given number of sensors are selected from among a fixed, but possibly very large, set of candidate locations. A systematic procedure is presented for finding optimal solutions through a relaxation of the original combinatorial problem, which boils down to determining an optimum spatial density of sensors instead of the actual locations. Thus a convex optimization problem with linear constraints is obtained. Its form makes it suitable for a solution using an extremely efficient algorithm of simplicial decomposition yielding an additional reduction in problem dimensionality. A technique is also discussed to post-process the computed optimal sensor density in order to get an equivalent form with minimal spatial support. The work is complemented with a numerical example and a discussion of various variants of the basic problem, which illustrates the generality and flexibility of the proposed approach.

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Authors and Affiliations

  1. University of Zielona Góra, Institute of Control and Computation Engineering, ul. Szafrana 2, 65-516, Zielona Góra, Poland

    Dariusz Uciński & Maciej Patan

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  1. Dariusz Uciński
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  2. Maciej Patan
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Correspondence to Dariusz Uciński .

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Editors and Affiliations

  1. Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

    Piotr Kulczycki

  2. Institute of Control and Computation Engineering, University of Zielona Góra, Zielona Góra, Poland

    Józef Korbicz

  3. Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

    Janusz Kacprzyk

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Uciński, D., Patan, M. (2021). Optimal Sensor Selection for Estimation of Distributed Parameter Systems. In: Kulczycki, P., Korbicz, J., Kacprzyk, J. (eds) Automatic Control, Robotics, and Information Processing. Studies in Systems, Decision and Control, vol 296. Springer, Cham. https://doi.org/10.1007/978-3-030-48587-0_11

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