Asymptotic stability of POD based model predictive control for a semilinear parabolic PDE

Abstract

In this article a stabilizing feedback control is computed for a semilinear parabolic partial differential equation utilizing a nonlinear model predictive (NMPC) method. In each level of the NMPC algorithm the finite time horizon open loop problem is solved by a reduced-order strategy based on proper orthogonal decomposition (POD). A stability analysis is derived for the combined POD-NMPC algorithm so that the lengths of the finite time horizons are chosen in order to ensure the asymptotic stability of the computed feedback controls. The proposed method is successfully tested by numerical examples.

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Correspondence to Stefan Volkwein.

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Alla, A., Volkwein, S. Asymptotic stability of POD based model predictive control for a semilinear parabolic PDE. Adv Comput Math 41, 1073–1102 (2015). https://doi.org/10.1007/s10444-014-9381-0

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Keywords

  • Dynamic programming
  • Nonlinear model predictive control
  • Asymptotic stability
  • Suboptimal control
  • Proper orthogonal decomposition

Mathematics Subject Classifications (2010)

  • 35K58
  • 49L20
  • 65K10
  • 90C30.