基于不变生成的到达-避免微分对策
Reach-Avoid Differential Games Based on Invariant Generation
摘要：
可达-避碰微分对策在飞行器避碰、运动规划与控制等方面有着重要的应用。核心问题是计算一组初态，自我玩家可以在指定的时间范围内执行安全规范的可满足性。以前的方法解决这个问题主要集中在有限的时间范围。我们研究这个问题的背景下，无限的时间范围内，自我球员的目的是永远迫使系统满足一定的安全规范，而相互的其他球员试图强制违反这一安全规范。在Hamilton Jacobi可达性框架下研究了该问题的唯一Lipschitz连续黏性解.该黏性解的连续性和唯一性使得可以利用当代的数值方法来求解具有适当数量的状态变量的问题。通过一个例子从摩尔Greitzer喷气发动机模型来说明我们的方法。
英文摘要：
Reach-avoid differential games play an important role in collision avoidance, motion planning and control of aircrafts, and related applications. The central problem is the computation of the set of initial states from which the ego player can enforce the satisfiability of safety specifications over a specified time horizon. Previous methods addressing this problem mostly focus on finite time horizons. We study this problem in the context of the infinite time horizon, where the ego player aims to perpetually force the system to satisfy certain safety specification while the mutual other player attempts to enforce a violation of this safety specification. The problem is studied within the Hamilton-Jacobi reachability framework with unique Lipschitz continuous viscosity solutions. The continuity and uniqueness property of the viscosity solution facilitates the use of contemporary numerical methods to solve this problem with an appropriate number of state variables. An example adopted from a Moore-Greitzer jet-engine model is employed to illustrate our approach.
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