RUI: Synthesis in Applications of Optimal Control

9971747Ledzewicz该项目包括两个部分，这两个部分都解决了在应用程序中出现的最优控制问题的常规合成问题。在第一部分中，将在场论的背景下研究异常极值的最优性的充分条件。一个泛化的扰动反馈控制法，允许将异常的轨迹到经典的框架将被用来构建一个本地定期合成异常参考极值。这些结构应该揭示一些最佳异常极值和奇异性（包括不连续性）的值函数的问题之间的连接。预计该项目的这一部分将有助于理论和应用的扰动反馈控制，定期综合，并通过提供推广，补充经典的结果，并成为重要的新工具，在应用中的最优性的充分条件。第二部分针对癌症化疗数学模型中一类低维非线性最优控制问题的精确和完整的解决方案。在模型中，细胞周期是通过将其不同的阶段聚集到隔室中并使用阶段特异性杀伤剂来控制的。在这个项目中，将对二室和三室模型进行全面分析。到目前为止，这些模型只是数值分析，但还没有得到定性或分析的结果结构的最优控制。预计，这些结果，有趣的也从理论的角度来看，将发现在数学模型中的应用程序调度癌症化疗protocols.The项目包括两个部分，这两个部分都解决的问题，找到完整的解决方案，在应用中出现的最优控制问题。第一种结构是由扰动反馈控制方案，在工程中，特别是在飞机控制设计的经典工具的动机。所提出的建设的目的是纳入所谓的异常轨迹，传统的计划是无效的。预计该项目的这一部分将通过提供补充经典结果的概括并成为应用中重要的新工具来为理论和应用做出贡献。在第二部分的项目模型的最优控制癌症化疗将进行调查。目标是最大限度地增加药物中细胞生长抑制剂杀死的癌细胞数量，同时保持对正常组织的毒性可接受。本项目将研究以前仅进行数值分析的一些模型，目的是获得完整的解析解。 预计这些结果，有趣的是，从理论的角度来看，将发现应用程序在数学模型中调度癌症化疗方案。

9971747LedzewiczThe project consists of two parts which both address the question of a regular synthesis for optimal control problems arising in applications. In the first part sufficient conditions for optimality of abnormal extremals will be investigated in the context of field theory. A generalization of the perturbation feedback control law that allows incorporating abnormal trajectories into the classical framework will be used to construct a local regular synthesis around an abnormal reference extremal. These constructions should shed some light on the connections between optimal abnormal extremals and singularities (including discontinuities) in the value function for the problem. It is expected that this part of the project will contribute to both theory and application of perturbation feedback control, regular synthesis, and sufficient conditions of optimality by providing generalizations that complement the classical results and become important new tools in applications. The second part addresses precise and complete solutions to a class of nonlinear optimal control problems in low dimensions arising in mathematical models for cancer chemotherapy. In the models the cell cycle is controlled by clustering its different phases into compartments and using phase specific killing agents. In this project a full analysis of two- and three-compartment models will be pursued. So far these models were only analyzed numerically, but no qualitative or analytic results about the structure of optimal controls have been obtained. It is expected that these results, interesting also from a theoretical point of view, will find applications in mathematical models for scheduling cancer chemotherapy protocols.The project consists of two parts which both address the question of finding full solutions to optimal control problems arising in applications. The first construction is motivated by the perturbation feedback control scheme, a classical tool in engineering, especially in aircraft control design. The proposed construction aims to incorporate so-called abnormal trajectories for which the conventional scheme is ineffective. It is expected that this part of the project will contribute to both theory and application by providing generalizations that complement the classical results and become important new tools in applications. In the second part of the project models of optimal control of cancer chemotherapy will be investigated. The goal is to maximize the number of cancer cells that a cytostatic agent in the drug kills while keeping the toxicity to the normal tissue acceptable. Some of the models that were only analyzed numerically before will be investigated in this project with the aim of obtaining a full analytic solution. It is expected that these results, interesting also from a theoretical point of view, will find applications in mathematical models for scheduling cancer chemotherapy protocols.