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Feed-back control of singularly perturbed heating problems

Part of the Lecture Notes in Mathematics book series (LNM,volume 711)

Abstract

In this paper the distribution of temperature is considered for a system for which the diffusion coefficient is small i.e. acts as a small parameter ɛ ↓ 0 and to which a feed-back control mechanism is applied based on the observation of temperature in a finite number of points. Some results are given concerning the following subjects:

  1. (i)

    construction of asymptotic approximations for ɛ ↓ 0 of solutions and proof of the correctness of these approximations

  2. (ii)

    stability of stationary states

  3. (iii)

    near optimal control using 1 observation point (optimal with respect to the criterion of minimizing a certain cost functional).

If relevant the obtained results are interpreted in terms of the physics of the problem. Moreover for some examples the results are graphically illustrated.

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References

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© 1979 Springer-Verlag

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van Harten, A. (1979). Feed-back control of singularly perturbed heating problems. In: Verhulst, F. (eds) Asymptotic Analysis. Lecture Notes in Mathematics, vol 711. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0062946

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  • DOI: https://doi.org/10.1007/BFb0062946

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09245-2

  • Online ISBN: 978-3-540-35332-4

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