Schwartz' distributions in nonlinear setting: application to differential equations, filtering and optimal control

Y. Orlov

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Schwartz' distributions in nonlinear setting: application to differential equations, filtering and optimal control

机译：非线性环境中的施瓦茨分布：在微分方程、滤波和最优控制中的应用

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The paper is intended to be of tutorial value for Schwartz' distributions theory in nonlinear setting. Mathematical models are presented for nonlinear systems which admit both standard and impulsive inputs. These models are governed by differential equations in distributions whose meaning is generalized to involve nonlinear, non single-valued operating over distributions. The set of generalized solutions of these differential equations is defined via closure, in a certain topology, of the set of the conventional solutions corresponding to standard integrable inputs. The theory is exemplified by mechanical systems with impulsive phenomena, optimal impulsive feedback synthesis, sampled-data filtering of stochastic and deterministic dynamic systems.

机译：本文旨在为非线性环境中的Schwartz分布理论提供指导价值。提出了非线性系统的数学模型，这些系统同时接受标准输入和脉冲输入。这些模型由分布中的微分方程控制，其含义被推广为涉及非线性、非单值的分布运算。这些微分方程的广义解集是通过在某种拓扑结构中对应于标准可积输入的常规解集的闭包来定义的。该理论以具有脉冲现象的机械系统、最优脉冲反馈合成、随机和确定性动态系统的采样数据滤波为例。

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《Mathematical Problems in Engineering: Theory, Methods and Applications》 |2002年第5期|367-387|共21页
作者
Y. Orlov;
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正文语种英语
中图分类工程数学;
关键词
Nonlinear dynamics; Distribution; Instantaneous impulse response; Generalized solution; Generalized feedback;

机译：非线性动力学;分销;瞬时脉冲响应;广义解;广义反馈;

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Schwartz' distributions in nonlinear setting: application to differential equations, filtering and optimal control

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