Lipschitz Continuity of the Value Function for the Infinite Horizon Optimal Control Problem Under State Constraints
Lipschitz Continuity of the Value Function for the Infinite Horizon Optimal Control Problem Under State Constraints
复制标题
状态约束下无限时域最优控制问题价值函数的Lipschitz连续性
DOI：
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发表时间：
2019
期刊：
影响因子：
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通讯作者：
H. Frankowska
中科院分区：
文献类型：
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作者：
V. Basco;H. Frankowska
本文研究了一类带状态约束的无限时域最优控制问题的值函数的Lipschitz正则性的充分条件。我们专注于问题的成本功能，包括贴现率因子，并允许时间依赖的动态和拉格朗日。此外，我们的状态约束可能是无界的和非光滑的边界。在我们的证明中使用的关键技术结果是对给定轨迹与其所有可行（可行）轨迹的距离的估计（假设贴现率足够大）。这些距离估计是根据统一的向内指向的条件下的状态约束，并意味着，特别是，可行的轨迹依赖于初始状态的Lipschitz的方式与时间的指数增加Lipschitz常数。作为推论，我们证明了原问题的值函数与松弛无限视界问题的值函数一致。
This paper investigates sufficient conditions for Lipschitz regularity of the value function for an infinite horizon optimal control problem subject to state constraints. We focus on problems with a cost functional that includes a discount rate factor and allow time dependent dynamics and Lagrangian. Furthermore, our state constraints may be unbounded and with nonsmooth boundary. The key technical result used in our proof is an estimate on the distance of a given trajectory from the set of all its viable (feasible) trajectories (provided the discount rate is sufficiently large). These distance estimates are derived under a uniform inward pointing condition on the state constraint and imply, in particular, that feasible trajectories depend on initial states in a Lipschitz way with an exponentially increasing in time Lipschitz constant. As a corollary, we show that the value function of the original problem coincides with the value function of the relaxed infinite horizon problem.
状态约束最优控制中改进的敏感性关系
影响因子：
1.8
作者：
Bettiol P
通讯作者：
Bettiol P