AI 中文总结
研究通过分布式反馈控制实现无人机运动角度稳定中的积分 - 微分方程，提出通用方法将其研究简化为常微分方程组分析，在指数稳定性上获新结果并应用于无人机飞行稳定。
AI 中文摘要
在本文中，我们提出使用积分算子形式的分布式反馈控制来实现无人机运动的角度稳定。需要强调的是，此积分算子的记忆可能是无界的。直观上，较长的观测时间为基于控制对象先前状态构建更好的控制开辟了新可能性。控制中的无界记忆需要创建一种不同于标准方法来研究积分 - 微分方程。本文的目标之一是提出一种通用方法，用于研究在指定稳定反馈控制的积分算子中存在无界记忆情况下积分 - 微分方程的稳定性。我们提出的方法能将积分 - 微分方程的研究简化为常微分方程组的分析。一般来说，这样的系统可能由无穷多个方程组成。在角度稳定问题的所谓线性近似中，在积分控制中设法限制在相对简单的指数核上，并得到一个有限方程数的系统。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。我们在积分 - 微分方程的指数稳定性方面获得了新的意外结果。然后将它们应用于无人机飞行的稳定。
英文摘要
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.
Comments22 pages, 5 Figures
