论文标题
迈向几何时间最小的控制，而没有legendre条件，并且具有多个奇异极端物质网络
Towards Geometric Time Minimal Control without Legendre Condition and with Multiple Singular Extremals for Chemical Networks
论文作者
论文摘要
本文讨论了通过控制温度最大化化学网络物种生产的问题。在所谓的质量动力学假设下，可以使用与反应网络关联的Feinberg-Horn-Jackson图将系统建模为单输入控制系统。得益于Pontryagin的最大原则，可以在极端曲线中找到候选人，而（非平滑）汉密尔顿动力学的解决方案可以说是与编辑端的终端目标的时间最小控制问题。使用几何控制和奇异理论，可以在通用条件下在终端歧管附近分类时间最小合成（闭环最佳控制）。在本文中，我们将重点放在不满足的广义Legendre-Clebsch条件下，这为具有几个单一弧形的复杂合成铺平了道路。特别是，它与弱可逆的网络（如两个反应的麦基坦方案）的情况有关。
This article deals with the problem of maximizing the production of a species for a chemical network by controlling the temperature. Under the so-called mass kinetics assumption the system can be modeled as a single-input control system using the Feinberg-Horn-Jackson graph associated to the reactions network. Thanks to Pontryagin's Maximum Principle, the candidates as minimizers can be found among extremal curves, solutions of a (non smooth) Hamiltonian dynamics and the problem can be stated as a time minimal control problem with a terminal target of codimension one. Using geometric control and singularity theory the time minimal syntheses (closed loop optimal control) can be classified near the terminal manifold under generic conditions. In this article we focus to the case where the generalized Legendre-Clebsch condition is not satisfied, which paves the road to complicated syntheses with several singular arcs. In particular it is related to the situation for a weakly reversible network like the McKeithan scheme of two reactions.
