A controlled model of carbon circulation between the atmosphere and the ocean
A controlled model of carbon circulation between the atmosphere and the ocean
复制标题
大气和海洋之间碳循环的受控模型
DOI：
10.1007/s10598-010-9081-7
复制
发表时间：
2010
影响因子：
--
通讯作者：
M. S. Nikol'skii
中科院分区：
文献类型：
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作者：
M. S. Nikol'skii
Kryazhimskii利用Svirezhev等人的结果开发了一个生物圈碳循环的受控模型，该模型允许全球范围内的人类活动。本文是对Kryazhimskii模型的数学研究。在第一部分中，我们计算函数x(T)的上确界≥0-大气中的碳量作为改变初始条件和相应微分方程式中系数的函数。在第二部分中，我们考虑了将碳排放减少到满足大气中碳浓度的给定限制条件的水平的经济成本最小化的问题。罚函数法被应用于确定与实际相关的特定情况下的最优控制之一的结构。这种特殊的最优控制最多只有一个开关点，并且处处取其两个极值之一(继电模式)。
A controlled model of the carbon cycle in the biosphere allowing for human activity on a global scale was developed by Kryazhimskii using the results of Svirezhev et al. The present article is a mathematical study of Kryazhimskii’s model. In the first part we calculate the supremum fort≥ 0 of the functionx(t)—the quantity of carbon in the atmosphere as a function of varying initial conditions and coefficients in the corresponding differential equations. In the second part we consider the problem of minimizing the economic costs of reducing carbon emissions to a level that meets given constraints on carbon concentration in the atmosphere. The penalty method is applied to determine the structure of one of the optimal controls for a particular case relevant in practice. This special optimal control has at most one switching point and everywhere takes one of its two extreme values (a relay mode).