发表机构
Rajiv Gandhi Institute of Petroleum Technology; University of Graz; Radon Institute for Computational and Applied Mathematics (RICAM)（拉吉夫·甘地石油技术学院; 格拉茨大学; 雷登计算与应用数学研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文分析带控制约束的HJI方程双层策略迭代的收敛性，并比较一阶与二阶HJB方程在有无约束控制下的数值解。
AI 中文摘要
分析了在存在控制约束时，满足Hamilton-Jacobi-Isaacs（HJI）方程的值函数的双层策略迭代算法的收敛性。考虑了对应于确定性和随机系统的一阶和二阶HJI方程。在数值测试中，应用了用于向后HJI偏微分方程的半隐式迎风方案，并针对无约束和有约束控制两种情况，对一阶和二阶Hamilton-Jacobi-Bellman（HJB）方程的解进行了全面比较。
英文摘要
Convergence of the bilevel policy iteration algorithm for the value function, satisfying the Hamilton-Jacobi-Isaacs (HJI) equation, is analyzed in the presence of control constraints. Both first and second-order HJI equations corresponding to the deterministic and stochastic systems are considered. For numerical tests, a semi-implicit upwind scheme for backward HJI PDEs is applied and a thorough comparison between the solutions to first and second-order Hamilton-Jacobi-Bellman (HJB) equations is presented for both the unconstrained and the constrained control cases.
Comments30 pages, 36 figures, Accepted in Computational and Applied Mathematics
