论文标题
凸汉密尔顿 - 雅各比 - 贝尔曼方程的弱解决方案的表示无限的地平线
Representation of Weak Solutions of Convex Hamilton-Jacobi-Bellman Equations on Infinite Horizon
论文作者
论文摘要
在本文中，为Infinite Horizon上一类进化的汉密尔顿 - 雅各比 - 贝尔曼方程的弱解决方案提供了代表性结果，汉密尔顿人可以在时间和纤维凸内进行测量。这样的哈密顿人与 - 忠实的代表性相关，即涉及可以在时间和控制中局部lipschitz的两个函数。我们的结果涉及在对纤维相对于纤维的Fenchel变换的轻松假设下的凸汉顿人的代表。我们将它们应用它们来研究一类时间依赖的汉密尔顿 - 雅各比 - 贝尔曼方程的弱解决方案的独特性，即消失在无穷大。假设上述Fenchel变换的域上具有生存力条件，这些弱解决方案被认为是在状态约束下无限范围控制问题的适当价值函数。
In the present paper, it is provided a representation result for the weak solutions of a class of evolutionary Hamilton-Jacobi-Bellman equations on infinite horizon, with Hamiltonians measurable in time and fiber convex. Such Hamiltonians are associated with a - faithful - representation, namely involving two functions measurable in time and locally Lipschitz in the state and control. Our results concern the recovering of a representation of convex Hamiltonians under a relaxed assumption on the Fenchel transform of the Hamiltonian with respect to the fiber. We apply them to investigate the uniqueness of weak solutions, vanishing at infinity, of a class of time-dependent Hamilton-Jacobi-Bellman equations. Assuming a viability condition on the domain of the aforementioned Fenchel transform, these weak solutions are regarded as an appropriate value function of an infinite horizon control problem under state constraints.
