Optimal Control of First-Order Hamilton–Jacobi Equations with Linearly Bounded Hamiltonian
Optimal Control of First-Order Hamilton–Jacobi Equations with Linearly Bounded Hamiltonian
复制标题
具有线性有界哈密顿量的一阶哈密顿-雅可比方程的最优控制
DOI：
10.1007/s00245-014-9239-3
复制
发表时间：
2013
影响因子：
1.8
通讯作者：
P. J. Graber
中科院分区：
文献类型：
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作者：
P. J. Graber
考虑一类一阶Hamilton-Jacobi方程解的最优控制问题，该方程的Hamilton-Jacobi方程是凸线性增长的。这个模型通过构建一个障碍物来控制前方的传播。我们证明了在松弛条件下该优化问题的极小值的存在性，并将极小值描述为耦合偏微分方程的平均场博弈型系统的弱解。进一步证明了PDE系统弱解的存在性和部分唯一性。本文还讨论了平均场博弈的解释。
We consider the optimal control of solutions of first order Hamilton–Jacobi equations, where the Hamiltonian is convex with linear growth. This models the problem of steering the propagation of a front by constructing an obstacle. We prove existence of minimizers to this optimization problem as in a relaxed setting and characterize the minimizers as weak solutions to a mean field game type system of coupled partial differential equations. Furthermore, we prove existence and partial uniqueness of weak solutions to the PDE system. An interpretation in terms of mean field games is also discussed.