Abstract We extend a sliding mode control methodology to linear evolution equations with uncertain but bounded inputs and noise in observations. We first describe the reachability set of the state equation in the form of an infinite-dimensional ellipsoid, and then steer the minimax center of this ellipsoid toward a finite-dimensional sliding surface in finite time by using the standard sliding mode output-feedback controller in equivalent form. We demonstrate that the designed controller is the best (in the minimax sense) in the class of all measurable functionals of the output. Our design is illustrated by two numerical examples: output-feedback stabilization of linear delay equations, and control of moments for an advection–diffusion equation in 2D.

中文翻译：

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具有噪声测量和不确定输入的线性演化方程的极小极大滑模控制设计

摘要 我们将滑模控制方法扩展到具有不确定但有界输入和观测噪声的线性演化方程。我们首先以无限维椭球的形式描述状态方程的可达集，然后通过使用标准滑模输出反馈控制器在有限时间内将该椭球的极小极大中心转向有限维滑动面等效形式。我们证明设计的控制器是输出的所有可测量泛函类中最好的（在极小极大意义上）。我们的设计通过两个数值例子来说明：线性延迟方程的输出反馈稳定，以及二维对流扩散方程的矩控制。