MULTISCALE SINGULAR PERTURBATIONS AND HOMOGENIZATION OF OPTIMAL CONTROL PROBLEMS
MULTISCALE SINGULAR PERTURBATIONS AND HOMOGENIZATION OF OPTIMAL CONTROL PROBLEMS
复制标题
多尺度奇异扰动和最优控制问题的均匀化
DOI：
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发表时间：
2007
期刊：
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通讯作者：
P. Bucci
中科院分区：
文献类型：
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作者：
O. Alvarez;M. Bardi;Claudio Marchi;P. Bucci
本文致力于研究具有有限数量尺度的奇异扰动问题，其中动力学和成本都可能振荡。在哈密顿量的一些矫顽力假设下，我们证明了值函数局部一致收敛于极限哈密尔顿-雅可比方程的有效柯西问题的解，并且有效算子保留了初始算子的几个性质；在一些附加假设下，显示了它们的明确公式。在一些特殊情况下，我们还描述了限制控制问题的有效动态和成本。一个重要的应用是具有有限数量尺度和强制哈密顿量的哈密顿-雅可比方程的均质化。
The paper is devoted to singular perturbation problems with a finite number of scales where both the dynamics and the costs may oscillate. Under some coercivity assumptions on the Hamiltonian, we prove that the value functions converge locally uniformly to the solution of an effective Cauchy problem for a limit Hamilton-Jacobi equation and that the effective operators preserve several properties of the starting ones; under some additional hypotheses, their explicit formulas are exhibited. In some special cases we also describe the effective dynamics and costs of the limiting control problem. An important application is the homogenization of Hamilton-Jacobi equations with a finite number of scales and a coercive Hamiltonian.