We consider an infinite horizon control problem for dynamics constrained to remain on a multidimensional junction with entry costs. We derive the associated system of Hamilton–Jacobi equations (HJ), prove the comparison principle and that the value function of the optimal control problem is the unique viscosity solution of the HJ system. This is done under the usual strong controllability assumption and also under a weaker condition, coined ‘moderate controllability assumption’.

中文翻译：

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带有进入成本的多维路口的最优控制的Hamilton–Jacobi方程

我们考虑了动力学的无限地平线控制问题，该问题被约束为与进入成本保持在多维交汇处。我们推导了汉密尔顿-雅各比方程（HJ）的关联系统，证明了比较原理，并且最优控制问题的值函数是HJ系统的唯一粘度解。这是在通常的强可控性假设下以及在较弱的条件（称为“中度可控性假设”）下完成的。