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Stabilizability of Parabolic Equations by Switching Controls Based on Point Actuators

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2026

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Kunisch, Karl
Rodrigues, Sérgio S.

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https://doi.org/10.1007/s00245-025-10381-0
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Austrian Science Fund (FWF): P 33432-NBL

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Applied Mathematics & Optimization. Springer. 2026, 93(2), 35. ISSN 0095-4616. eISSN 1432-0606. Verfügbar unter: doi: 10.1007/s00245-025-10381-0

Zusammenfassung

It is shown that a switching control involving a finite number of Dirac delta actuators is able to steer the state of a general class of nonautonomous parabolic equations to zero as time increases to infinity. The strategy is based on a recent feedback stabilizability result, which utilizes control forces given by linear combinations of appropriately located Dirac delta distribution actuators. Then, the existence of a stabilizing switching control with no more than one actuator is active at each time instant is established. For the implementation in practice, the stabilization problem is formulated as an infinite-horizon optimal control problem, with cardinality-type control constraints enforcing the switching property. Subsequently, this problem is tackled using a receding horizon framework. Its suboptimality and stabilizing properties are analyzed. Numerical simulations validate the approach, illustrating its stabilizing and switching properties.

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510 Mathematik

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ISO 690AZMI, Behzad, Karl KUNISCH, Sérgio S. RODRIGUES, 2026. Stabilizability of Parabolic Equations by Switching Controls Based on Point Actuators. In: Applied Mathematics & Optimization. Springer. 2026, 93(2), 35. ISSN 0095-4616. eISSN 1432-0606. Verfügbar unter: doi: 10.1007/s00245-025-10381-0
BibTex
@article{Azmi2026-04Stabi-76337,
  title={Stabilizability of Parabolic Equations by Switching Controls Based on Point Actuators},
  year={2026},
  doi={10.1007/s00245-025-10381-0},
  number={2},
  volume={93},
  issn={0095-4616},
  journal={Applied Mathematics & Optimization},
  author={Azmi, Behzad and Kunisch, Karl and Rodrigues, Sérgio S.},
  note={Article Number: 35}
}
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