椭球运动的状态约束问题
State Constrain Problem of Ellipsoidal Motions
DOI: 10.12677/PM.2022.121021, PDF,    国家自然科学基金支持
作者: 敬鲁晶, 高红伟, 侯 敏：青岛大学数学与统计学院，山东 青岛
关键词: 编队控制；椭球运动；状态约束；目标集；Hamilton-Jacobi-Bellman方程；Formation Control； Virtual Ellipsoid Motion； State Constrains； Target Set； HJB Equation
摘要: 本文研究了椭球运动的状态约束问题，其中椭球可以在状态约束作用下向给定目标集运动。利用Hamilton-Jacobi-Bellman (HJB)方程，给出了状态约束问题的闭环解。最后，给出求解方法以及数值算例。仿真结果表明，状态约束能够保证椭球在合理的状态范围内，最终运动到达目标集。
Abstract: The paper deals with the problem of state constrain of ellipsoidal motion, where the virtual ellipsoid can move to the target set under state constrain. We present solutions of this problem in the class of closed-loop (feedback) controls based on Hamilton-Jacobi-Bellman (HJB) equation. Finally, we give a solution method and numerical examples. Simulation results verify that the state constraint can ensure that the ellipsoidal motions within a reasonable range of states and finally reaches the target set.
文章引用：敬鲁晶, 高红伟, 侯敏. 椭球运动的状态约束问题[J]. 理论数学, 2022, 12(1): 165-173. https://doi.org/10.12677/PM.2022.121021

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