Blowup Time Optimal Control for Ordinary Differential Equations
Blowup Time Optimal Control for Ordinary Differential Equations
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DOI：
10.1137/090764232
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
P. Lin;GengshengBB Wang
中科院分区：
文献类型：
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作者：
P. Lin;GengshengBB Wang
研究了一类由经典非线性常微分方程控制系统所支配的时间最优控制问题。对应于一定的控制，系统的解具有爆破行为，即在有限时刻爆破。控制系统的目标是最小化爆破时间。因此，本文研究的时间最优控制问题将其目标集保持在其状态空间之外。从这个角度来看，它本质上区别于大多数时间最优控制问题的研究，从过去的出版物。本文通过对一类典型时间最优控制问题的分析，提出了一种新的时间最优控制存在性的证明方法。我们还旨在创建一个新的方法来建立最优控制的庞特里亚金最大值原理。本文的主要结果可以推广到非线性项具有更一般形式的受控系统。
This paper studies a time optimal control problem governed by a classical controlled system of nonlinear ordinary differential equations. Corresponding to certain controls, the solutions of the system have the behavior of blowup; namely, they blow up at a finite time. The goal for controlling the system is to minimize the blowup time. Therefore, the time optimal control problem studied in this paper holds its target set outside of its state space. From this perspective, it essentially differentiates from the most time optimal control problems in studies from past publications. The purpose of this study is to develop a new method for proving the existence of time optimal controls for such kinds of time optimal control problems through analyzing a typical problem. We also aim to create a new method for establishing the Pontryagin maximum principle of optimal controls. The main results derived from this paper can be extended to controlled systems, where nonlinear terms have a more general form, by the two methods mentioned above.