Integro-differential equations in angular stabilization of drone motion by distributed feedback control
Integro-differential equations in angular stabilization of drone motion by distributed feedback control
利用分布式反馈控制实现无人机姿态稳定的积分微分方程研究
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.
摘要： 在本文中，我们提出了一种利用积分算子形式的分布式反馈控制来实现无人机姿态稳定的方法。需要强调的是，该积分算子的记忆长度可以是无限的。直观上，较长的观测时间为基于控制对象历史状态构建更优控制策略提供了新的可能性。控制中无限记忆的特性要求我们建立一种不同于标准方法的新途径，以研究此类积分微分方程。
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.
本文的目标之一是提出一种通用的方法，用于研究在反馈控制中积分算子具有无限记忆的情况下，积分微分方程的稳定性。我们提出的方法可以将对积分微分方程的研究简化为对常微分方程组的分析。通常情况下，此类方程组可能包含无穷多个方程。
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.
在角度稳定问题的线性近似处理中，我们成功地将积分控制限制在相对简单的指数核上，从而得到了一个有限方程组。文中示例表明，更复杂的核（例如指数核的线性组合）可以增强稳定能力。我们获得了关于积分微分方程指数稳定性的新颖且出人意料的结果，并将其应用于无人机飞行稳定控制中。
Article Details:
- Authors: Alexander Domoshnitsky, Oleg Kupervasser, Anatoly Polonsky
- Subjects: Artificial Intelligence (cs.AI); Machine Learning (cs.LG); Optimization and Control (math.OC)
- arXiv ID: 2607.18251
文章详情：
- 作者： Alexander Domoshnitsky, Oleg Kupervasser, Anatoly Polonsky
- 学科分类： 人工智能 (cs.AI)；机器学习 (cs.LG)；优化与控制 (math.OC)
- arXiv 编号： 2607.18251