HIV病毒动力学的自由最终时间最优控制

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摘要翻译：
在这篇论文中，我们检验了HIV野生型感染的一个成熟的模型。给出了固定最终时间的最速下降法的算法，并提出了自由最终时间的改进方法。第一类成本功能考虑，寻求最小化治疗的总时间。这个问题的一个简单实施表明，由于最佳控制的“先打后打”性质，它在治疗的早期阶段以及基于个人的研究中都是有效的。提出了一种基于LQR的代价泛函，并用最速下降法求解。提示最佳治疗方法必须保持在较高水平，直到患者出现恢复迹象，之后治疗逐渐减少。这符合生物医学哲学。用改进的算法近似求解一个包含总时间权重的修正问题。它显示总期间有相当大的下降。我们的结论是，减少和优化治疗周期可以帮助我们提高效率和病人护理的周转率。
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英文标题：
《Free Final-Time Optimal Control for HIV Viral Dynamics》
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作者：
Gaurav Pachpute, Kriti Saxena
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最新提交年份：
2011
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分类信息：

一级分类：Mathematics        数学
二级分类：Optimization and Control        优化与控制
分类描述：Operations research, linear programming, control theory, systems theory, optimal control, game theory
运筹学，线性规划，控制论，系统论，最优控制，博弈论
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一级分类：Quantitative Biology        数量生物学
二级分类：Other Quantitative Biology        其他定量生物学
分类描述：Work in quantitative biology that does not fit into the other q-bio classifications
不适合其他q-bio分类的定量生物学工作
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英文摘要：
  In this paper, we examine a well-established model for HIV wild-type infection. The algorithm for steepest descent method for fixed final-time is stated and a modified method for free final-time is presented. The first type of cost functional considered, seeks to minimize the total time of therapy. An easy implementation for this problem suggests that it can be effective in the early stages of treatment as well as for individual-based studies, due to the "hit first and hit hard" nature of optimal control.   An LQR based cost functional is also presented and the solution is found using steepest descent method. It suggests that the optimal therapy must remain high until the patient shows signs of recovery after which, the therapy gradually decreases. This is in line with the biomedical philosophy. Solution to a modified problem which includes a weight for total time is approximated using the modified algorithm. It shows a considerable drop in the total period. We conclude that, a decreased and optimized therapy period can help us increase efficiency as well as the turnover rate for patient care.
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PDF链接：
https://arxiv.org/pdf/1110.3398

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关键词：最优控制 动力学 HIV Quantitative Optimization cost total modified descent 病人