In the paper, for systems described by ordinary differential equations a review of algorithms of dynamical input reconstruction by results of inaccurate observations of its solutions is given. The problem under discussion is referred to the class of dynamical inverse problems. The proposed algorithms are stable with respect to informational noises and computational errors. They are based on the combination of methods of the theory of ill-posed problems and the theory of feedback control. The essence of the methodology underlying the algorithms suggested in the paper consists in the representation of a reconstruction algorithm in the form of a feedback control algorithm for a certain artificial dynamical system, a model; such an algorithm, whose output is the realization of the control in the model, is dynamical by its definition.

中文翻译：

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常微分方程系统中输入的动态重构方法

在本文中，对于由常微分方程描述的系统，通过对其解决方案的不精确观察结果，对动态输入重构算法进行了综述。讨论中的问题称为动态逆问题类。所提出的算法对于信息噪声和计算误差是稳定的。它们基于不适定问题理论和反馈控制理论的方法的结合。本文提出的算法所基于的方法论的实质在于，对于某种人工动力系统，模型，以反馈控制算法的形式表示重构算法。这种算法的定义是动态的，其输出是模型中控件的实现。