We present some results concerning the control of the Burgers equation. We analyze a bi-objective optimal control problem and then the hierarchical null controllability through a Stackelberg–Nash strategy, with one leader and two followers. The results may be viewed as an extension to this nonlinear setting of a previous analysis performed for linear and semilinear heat equations. They can also be regarded as a first step in the solution of control problems of this kind for the Navier–Stokes equations.

中文翻译：

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Burgers 方程的双目标分层控制

我们提出了一些关于伯格斯方程控制的结果。我们分析了双目标最优控制问题，然后通过 Stackelberg-Nash 策略（有一个领导者和两个追随者）分析了分层零可控性。结果可以被视为对线性和半线性热方程先前分析的非线性设置的扩展。它们也可以被视为解决纳维-斯托克斯方程此类控制问题的第一步。