Adaptive control of a flexible satellite with an internal disturbance

Billal Lekdim; Billal Lekdim

doi:10.3934/mmc.2026014

Mathematical Modelling and Control

2026, Volume 6, Issue 2: 185-193. doi: 10.3934/mmc.2026014

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Research article

Adaptive control of a flexible satellite with an internal disturbance

Billal Lekdim ^{1,2
,
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1.
Faculty of Exact Sciences and Computer Science, University of Djelfa, PO Box 3117, Djelfa 17000, Algeria
2.
SD Laboratory, Faculty of Mathematics, University of Science and Technology Houari Boumediene, PO Box 32, El-Alia, Bab Ezzouar, 16111, Algiers, Algeria

Received: 09 April 2025 Revised: 12 August 2025 Accepted: 17 September 2025 Published: 08 June 2026

This paper examines the well-posedness and adaptive stabilization of a satellite vibration caused by internal disturbances. The structure of the satellite is made up of two flexible, symmetrical wings that are connected to a central body. The wings are modeled as transmission Euler-Bernoulli beams with dynamic boundary conditions. We design high-gain adaptive regulators by measuring velocity feedback at the central body to quickly dampen vibrations. We demonstrate an exponential decay result for the system employing the multiplier method. The theoretical results are supported by a numerical simulation.
- flexible satellite,
- adaptive control,
- exponential decay,
- Euler-Bernoulli beams
Citation: Billal Lekdim. Adaptive control of a flexible satellite with an internal disturbance[J]. Mathematical Modelling and Control, 2026, 6(2): 185-193. doi: 10.3934/mmc.2026014

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Abstract

This paper examines the well-posedness and adaptive stabilization of a satellite vibration caused by internal disturbances. The structure of the satellite is made up of two flexible, symmetrical wings that are connected to a central body. The wings are modeled as transmission Euler-Bernoulli beams with dynamic boundary conditions. We design high-gain adaptive regulators by measuring velocity feedback at the central body to quickly dampen vibrations. We demonstrate an exponential decay result for the system employing the multiplier method. The theoretical results are supported by a numerical simulation.

References

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