Representation of Hamilton–Jacobi Equation in Optimal Control Theory with Unbounded Control Set
提出新方法构造一类更广泛的Hamiltonian的表征，不要求Legendre-Fenchel共轭有界，从而得到无界控制集的表征，并应用于研究值函数正则性及变分与最优控制问题的关联。
Abstract In this paper, we study the existence of sufficiently regular representations of Hamilton–Jacobi equations in the optimal control theory with unbounded control set. We use a new method to construct representations for a wide class of Hamiltonians. This class is wider than any constructed before, because we do not require Legendre–Fenchel conjugates of Hamiltonians to be bounded. However, in this case we obtain representations with unbounded control set. We apply the obtained results to study regularities of value functions and correlations between variational and optimal control problems.