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arXiv 2302.02658math.OC
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一类输入为L1约束的平面L $\infty$最优控制问题的最优综合

Optimal synthesis for a class of L $\infty$ optimal control problems in the plane with L 1 constraint on the input

Emilio Molina, Alain Rapaport

摘要:

对于一类特殊的平面动力学是线性的控制变量,我们表明,反馈策略“零奇异零”是最小化的最大值的坐标在无限的地平线上,下的L1预算约束的控制。此外,我们将最优成本描述为预算的函数。证明是基于一个不寻常的使用时钟的形式。这一结果推广了以前获得的SIR流行病模型更一般的Kolmogorov动力学,我们说明其他生物模型。

英文摘要:

For a particular class of planar dynamics that are linear with respect to the control variable, we show that the feedback strategy ''null-singular null'' is minimizing the maximum of a coordinate over infinite horizon, under a L 1 budget constraint on the control. Moreover, we characterize the optimal cost as a function of the budget. The proof is based on an unusual use of the clock form. This result generalizes the one obtained formerly for the SIR epidemiological model to more general Kolmogorov dynamics, that we illustrate on other biological models.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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