A control problem for an operator differential equation in a Hilbert space is considered. The problem consists in constructing an algorithm generating a feedback control and guaranteeing that the solution of the equation follows a solution of another equation, which is subject to an unknown disturbance. We assume that both equations are given on an infinite time interval and the unknown disturbance is an element of the space of square integrable functions; i.e., the perturbation may be unbounded. We construct two algorithms based on elements of the theory of ill-posed problems and the extremal shift method known in the theory of positional differential games. The algorithms are stable with respect to information noises and calculation errors. The first and second algorithms can be used in the cases of continuous and discrete measurement of solutions, respectively.

中文翻译：

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跟踪算子微分方程解的问题中的极值移位

考虑希尔伯特空间中算子微分方程的控制问题。问题在于构造一种算法，该算法生成反馈控制并确保方程的解遵循另一个方程的解，该方程受到未知干扰。我们假设两个方程都是在无限的时间间隔上给出的，未知扰动是平方可积函数空间的一个元素。即，摄动可能是无限的。我们基于不适定问题理论的元素和位置差分博弈理论中已知的极值移位方法构造了两种算法。该算法在信息噪声和计算误差方面是稳定的。