It has been shown in previous works that an optimal control formulation for an incompressible ideal fluid flow yields Euler's fluid equations. In this paper we consider the modified Euler's equations by adding a potential function playing the role of a barrier function in the corresponding optimal control problem with the motivation of studying obstacle avoidance in the motion of fluid particles for incompressible ideal flows of an inviscid fluid From the physical point of view, imposing an artificial potential in the fluid context is equivalent to generating a desired pressure. Simulation results for the obstacle avoidance task are provided.

翻译：已有研究表明，不可压缩理想流体流动的最优控制形式可推导出欧拉流体方程。本文通过在相应最优控制问题中引入一个势函数作为障碍函数，研究不可压缩无粘流体理想流动中流体粒子运动的避障问题，从而得到修正的欧拉方程。从物理角度看，在流体环境中施加人工势函数等价于产生所需的压力场。文中给出了避障任务的仿真结果。