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Numerical algorithms for hierarchical optimization for estimating parameters in state and control constrained optimal control problems.

用于估计状态和控制约束最优控制问题中的参数的分层优化的数值算法。

基本信息

批准号：
242358572
负责人：
Professor Dr. Hans Georg Bock
金额：
--
依托单位：
Interdisziplinäres Zentrum für Wissenschaftliches Rechnen (IWR)
依托单位国家：
德国
项目类别：
Research Grants
财政年份：
2013
资助国家：
德国
起止时间：
2012-12-31 至 2017-12-31
项目状态：
已结题

来源：
https://gepris.dfg.de/gepris/projekt/242358572?language=en
关键词：
Numerical algorithms hierarchical optimization estimating

项目摘要

In this project, we investigate hierarchical optimization problems with a parameter estimation problem on the upper level and a nonlinear control and state constrained optimal control problem (OCP) with boundary and interior point conditions on the lower level.The goal of this project is to derive mathematical methods for numerically solving this class of problems. In particular, the reliable treatment of state and control constraints in the lower level problem has to be ensured.Therefore, we firstly discretize the optimal control problem on the lower level appropriately. Afterwards, we derive first order optimality conditions of the discretized OCP, and replace the lower level problem by them. This leads to a structured mathematical program with equilibrium constraints (MPEC), which requires a special treatment since it violates standard regularity assumptions in mathematical optimization (like the "linear independence constraint qualification") at every feasible point. For solving the MPEC, we derive a structure exploiting mathematical method which is tailored to this problem class. This method combines sequential linear programing with quadratic programing in order to ensure the desired stationarity properties in the solution.The methods we derive in this project have to be constructed such that potential applications of bi-level optimization problems with optimal control problems on the lower level in fields like medicine, robotics or biomechanics, where this problem setting is often called "inverse optimal control", can be solved.

在本计画中，我们研究上层为参数估计问题，下层为非线性控制与状态约束最优控制问题（OCP），目标是推导出数值求解这类问题的数学方法。特别是，必须确保低层问题中状态和控制约束的可靠处理，因此我们首先将低层最优控制问题适当离散化。然后，我们推导了离散化最优控制问题的一阶最优性条件，并用它们代替了下层问题。这导致了一个带有平衡约束的结构化数学规划（MPEC），它需要特殊的处理，因为它在每个可行点都违反了数学优化中的标准正则性假设（如“线性独立约束资格”）。为了解决MPEC，我们推导出一个结构，利用数学方法，这是针对这个问题的类。这种方法结合了序列线性规划和二次规划，以确保所需的平稳性的解决方案，我们在这个项目中得到的方法必须构造，使潜在的应用的双层优化问题与最优控制问题的低级别在医学，机器人或生物力学等领域，在这种问题的设置通常被称为“逆最优控制”，可以解决。