Integro-differential equations in angular stabilization of drone motion by distributed feedback control
This paper proposes angular stabilization of drone motion using distributed feedback control in the form of an integral operator with possibly unbounded memory. The authors introduce a universal approach to study stability of integro-differential equations, reducing them to systems of ordinary differential equations. For linear approximation in angle stabilization, simple exponential kernels lead to finite systems, while more complex kernels can enhance stabilization. New results on exponential stability are obtained and applied to drone stabilization.
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[Submitted on 10 May 2026]
Title:Integro-differential equations in angular stabilization of drone motion by distributed feedback control
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Abstract:In this paper, we propose angular stabilization of drone motion using distributed feedback control in the form of an integral operator. It should be stressed that the memory of this integral operator could be unbounded. It is intuitively clear that large length of the observation time open new possibilities to construct better control based on previous states of the control object. Unbounded memory in control requires the creation of a certain approach different from standard ones to the study of integro-differential equations. One of the goals of this article is to propose a certain universal approach that allows us to study the stability of integro-differential equations in the case of unbounded memory in the integral operator specifying the feedback control in stabilization. The approach we propose allows us to reduce the study of integro-differential equations to the analysis of systems of ordinary differential equations. In general, such systems can consist of an infinite number of equations. In relation to the so-called linear approximation in the problem of angle stabilization manages to limit itself to relatively simple exponential kernels in the integral control and arrive at a system with a finite number of equations. The examples explain that more complex kernels, for example, linear combinations of the exponential kernels, can enhance the stabilization capabilities. We obtain new unexpectable results on the exponential stability of integro-differential equations. Then we apply them to stabilization of drone flight.
Comments: 22 pages, 5 Figures
Subjects:
Artificial Intelligence (cs.AI); Machine Learning (cs.LG); Optimization and Control (math.OC)
Cite as: arXiv:2607.18251 [cs.AI]
(or arXiv:2607.18251v1 [cs.AI] for this version)
https://doi.org/10.48550/arXiv.2607.18251
arXiv-issued DOI via DataCite
Submission history
From: Oleg Kupervasser [view email] [v1] Sun, 10 May 2026 14:16:45 UTC (234 KB)
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