Continuity of Pontryagin Extremals with Respect to Delays in Nonlinear Optimal Control
Continuity of Pontryagin Extremals with Respect to Delays in Nonlinear Optimal Control
复制标题
非线性最优控制中庞特里亚金极值相对于时滞的连续性
DOI：
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发表时间：
2018
期刊：
影响因子：
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通讯作者：
E. Trélat
中科院分区：
文献类型：
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作者：
Riccardo Bonalli;Bruno Hérissé;E. Trélat
考虑一个有限维的一般非线性最优控制问题，具有常数状态和/或控制时滞。根据庞特里亚金最大值原理，任何最优轨迹都是庞特里亚金极值的投影。我们建立，在适当的假设下，庞特里亚金极值连续依赖于参数延迟，适当的拓扑结构。轨迹的连续性和控制的连续性的证明是相当容易的，然而，对于伴随向量，证明需要更精细的分析。伴随关于参数延迟的连续性为间接方法的数值实现（如打靶法）开辟了一个新的视角。我们还讨论了我们假设的清晰度。
Consider a general nonlinear optimal control problem in finite dimension, with constant state and/or control delays. By the Pontryagin Maximum Principle, any optimal trajectory is the projection of a Pontryagin extremal. We establish that, under appropriate assumptions, Pontryagin extremals depend continuously on the parameter delays, for adequate topologies. The proof of the continuity of the trajectory and of the control is quite easy, however, for the adjoint vector, the proof requires a much finer analysis. The continuity property of the adjoint with respect to the parameter delay opens a new perspective for the numerical implementation of indirect methods, such as the shooting method. We also discuss the sharpness of our assumptions.