We consider output tracking for a class of viscous nonlinear fluid flows including the incompressible 2D Navier–Stokes equations. The fluid is subject to in-domain inputs and disturbances. We construct an error feedback controller which guarantees approximate local velocity output tracking for a class of reference outputs. The control solution covers point velocity observations and assumes a smooth enough state space. Efficacy of the control solution is illustrated through a numerical example.

中文翻译：

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一类非线性流体流动的近似局部输出调节

我们考虑对一类粘性非线性流体流动的输出跟踪，包括不可压缩的 2D Navier-Stokes 方程。流体会受到域内输入和干扰。我们构造了一个误差反馈控制器，它保证对一类参考输出的近似局部速度输出跟踪。控制解决方案涵盖点速度观测并假设足够平滑的状态空间。通过一个数值例子说明了控制解决方案的有效性。