化学网络无Legendre条件多奇异点的几何时间最小控制
Towards Geometric Time Minimal Control without Legendre Condition and with Multiple Singular Extremals for Chemical Networks
摘要：
本文讨论了通过控制温度使化学网络中的物种产量最大化的问题。在所谓的质量动力学假设下，可以使用与反应网络相关联的Feinberg-Horn-Jackson图将系统建模为单输入控制系统。由于庞特里亚金的最大值原理，作为最小值的候选人，可以发现之间的极值曲线，解决方案的（非光滑）哈密顿动力学和问题可以说是一个时间最小的控制问题的终端目标的余维1。利用几何控制和奇异性理论，在一般条件下，时间最小综合（闭环最优控制）可以在终端流形附近分类。在这篇文章中，我们专注于广义Legendre-Clebsch条件不满足的情况下，这铺平了道路，复杂的合成与几个奇异弧。特别是它涉及到的情况下，弱可逆网络一样的麦基森计划的两个反应。
英文摘要：
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.
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