计算移动目标的最小时间拦截
Computing the Minimum-Time Interception of a Moving Target
AI总结：
本文提出一种求解移动目标最小时间拦截最优控制问题的算法框架，利用到可达集距离的解析描述保证收敛，并在Dubins车等模型上验证了其有效性。
摘要：
在本研究中，我们提出了一种用于解决一类最优控制问题的算法框架。该类问题与移动目标的最小时间拦截问题相关，其中具有给定状态方程的受控对象必须接近一个轨迹预先已知的移动目标。我们的框架利用了对任意点到受控对象可达集距离的解析描述。所提出的算法始终收敛，并且在不丧失对任意Lipschitz连续移动目标轨迹收敛到正确解的保证的情况下，无法对其进行改进。在实践中，对于受控对象的复杂状态方程，难以获得到可达集距离的解析描述。然而，研究表明，对于一些广泛使用的模型，如Dubins车，该距离可以以显式形式获得。最后，我们通过简单运动和Dubins模型说明了所提出框架的通用性和有效性。
英文摘要：
In this study, we propose an algorithmic framework for solving a class of optimal control problems. This class is associated with the minimum-time interception of moving target problems, where a plant with a given state equation must approach a moving target whose trajectory is known a priori. Our framework employs an analytical description of the distance from an arbitrary point to the reachable set of the plant. The proposed algorithm is always convergent and cannot be improved without losing the guarantee of its convergence to the correct solution for arbitrary Lipschitz continuous trajectories of the moving target. In practice, it is difficult to obtain an analytical description of the distance to the reachable set for the sophisticated state equation of the plant. Nevertheless, it was shown that the distance can be obtained for some widely used models, such as the Dubins car, in an explicit form. Finally, we illustrate the generality and effectiveness of the proposed framework for simple motions and the Dubins model.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
