Optimal and receding horizon control of tumor growth in myeloma bone disease
Optimal and receding horizon control of tumor growth in myeloma bone disease
复制标题
骨髓瘤骨病肿瘤生长的最佳控制和后退控制
DOI：
10.1016/j.bspc.2015.10.004
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发表时间：
2016
期刊：
影响因子：
--
通讯作者：
S. Vinga
中科院分区：
文献类型：
--
作者：
J. M. Lemos;D. Caiado;R. Coelho;S. Vinga
本文讨论了骨髓瘤骨病的治疗设计问题，以系统的方式优化药物毒性和肿瘤抑制之间的妥协。为此，最优控制的技术被应用到肿瘤生长的动力学，并使用数值松弛算法解决庞特里亚金的最小值原理的必要条件。基于PI控制规则，并行应用加速骨量恢复的治疗。由于最优控制器提供开环控制，因此通过遵循滚动时域策略将其转化为反馈律。为此，首先在时间范围内计算最佳操纵变量分布，但仅应用该函数的初始部分。然后，在对应于先前应用的控制的结束的时刻开始重复整个优化过程。
This article addresses the problem of designing therapies for the myeloma bone disease that optimize in a systematic way a compromise between drug toxicity and tumor repression. For that sake, the techniques of optimal control are applied to the dynamics of tumor growth, and the necessary conditions of Pontryagin's minimum principle are solved using a numerical relaxation algorithm. A therapy to accelerate bone mass recovery is applied in parallel, based on a PI control rule. Since the optimal controller provides an open-loop control, it is turned into a feedback law by following a receding horizon strategy. For that sake, an optimal manipulated variable profile is first computed over a time horizon, but only the initial part of this function is applied. The whole optimization procedure is then repeated starting at a time instant that corresponds to the end of the previously applied control.