On quadratic approximations for Hamilton-Jacobi-Bellman equations

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• 作者：Yumiharu Nakano ^{nakano.y.ai@m.titech.ac.jp" class="auth_mail" title="E-mail the corresponding author}Author Vitae
• 关键词：Hamilton&ndash ; Jacobi&ndash ; Bellman equations ; Quadratic approximations ; Stochastic control ; Partial differential equations ; Error analysis
• 刊名：Automatica
• 出版年：2016
• 出版时间：April 2016
• 年：2016
• 卷：66
• 期：Complete
• 页码：205-217
• 全文大小：811 K

文摘

We study simple quadratic approximations for general Hamilton–Jacobi–Bellman equations. The theoretical error bounds are shown to be composed of the time discretization errors and quadratic approximation ones at each time step. Several numerical experiments show that the quadratic approximations work for the equations with the boundary and Hamiltonian well approximated by the quadratic functions.