An ergodic control problem is studied for controlled linear stochastic equations driven by cylindrical Lévy noise with unbounded control operator in a Hilbert space. A family of optimal controls is shown to consist of those asymptotically achieving the feedback form that employs the corresponding Riccati equation. The formula for optimal cost is given. The general results are applied to stochastic heat equation with boundary control and to stochastic structurally damped plate equations with point control.

中文翻译：

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圆柱Lévy过程驱动的线性随机PDE的遍历边界和点控制

研究了在Hilbert空间中由圆柱Lévy噪声和无界控制算子驱动的受控线性随机方程的遍历控制问题。一系列最优控制已显示为包括渐近实现采用相应Riccati方程的反馈形式的控制。给出了最佳成本的公式。将一般结果应用于带边界控制的随机热方程和带点控制的随机结构阻尼板方程。