混合最优控制问题中达到目标集时间的连续性和唯一性
The continuity and uniqueness of the value function of the hybrid optimal control problem with reach time to a target set
AI总结：
本文研究了混合最优控制问题中达到目标集时间的价值函数连续性和唯一性，通过动态规划原理证明其连续性，并将其表征为粘性意义下的拟变分不等式唯一解。
摘要：
本文研究了具有到达目标集时间的混合最优控制问题，并证明了相关价值函数的连续性和唯一性。混合系统涉及连续和离散动力学的相互作用。连续系统的状态由常微分方程演化，直到轨迹击中预定义的跳跃集：一个自主跳跃集和一个受控跳跃集。在每次跳跃时，轨迹会通过离散系统断续地转移到另一个欧几里得空间。我们研究了具有到达时间的目标集的混合最优控制问题，证明了在假设下价值函数关于初始点的连续性，并利用动态规划原理将其表征为粘性意义下的拟变分不等式的唯一解。
英文摘要：
The hybrid optimal control problem with reach time to a target set is addressed and the continuity and uniqueness of the associated value function is proved. Hybrid systems involves interaction of different types of dynamics: continuous and discrete dynamics. The state ofa continuous system is evolved by an ordinary differential equation until the trajectory hits the predefined jump sets: an autonomous jump set and a controlled jump set . At each jump the trajectory is moved discontinuously to another Euclidean space by a discrete system. We study the hybrid optimal control problem with reach time to a target set, prove the continuity of the associated value function with respect to the initial point under the assumption that is lower semicontinuous on the boundary of a target set, and also characterize it as an unique solution of a quasi-variational inequality in a viscosity sense using the dynamic programming principle.
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