ESTIMATING PARAMETERS IN OPTIMAL CONTROL PROBLEMS
ESTIMATING PARAMETERS IN OPTIMAL CONTROL PROBLEMS
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DOI：
10.1137/110823390
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发表时间：
2012-01-01
影响因子：
3.1
通讯作者：
Bock, Hans Georg
中科院分区：
文献类型：
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作者：
Hatz, Kathrin;Schloeder, Johannes P.;Bock, Hans Georg
在自然界中，有许多过程被认为是最佳运行的，例如，人类的运动，特别是人类的步态。在本文中，我们考虑了这类过程的模型，这些模型可以用最优控制问题来描述。这些模型的特点是数量未知且无法测量(例如系统参数或最优性标准的构成)。我们的目标是从测量数据中确定这些未知量，这相当于解决基于最优控制模型的参数估计问题。我们研究了两种求解递阶优化问题的方法；这两种方法都遵循了用最优性条件代替底层最优控制问题的思想。第一种方法基于庞特里亚金最大值原理，而第二种方法使用直接多次激发和相应的Karush-Kuhn-Tucker条件。这两种方法都提出了本文讨论的数值挑战。最后，我们通过一个基准问题来考察我们的方法的性能。
In nature, there are many processes that are assumed to run optimally, for example, human motion or, in particular, human gait. In this paper, we consider models of such processes, which can be described by optimal control problems. These models are characterized by quantities that are not known and cannot be measured (examples are system parameters or the constitution of the optimality criterion). Our goal is to determine these unknown quantities from measurement data, which is equivalent to solving a parameter estimation problem based on an optimal control model. We investigate two approaches for finding the solution of this hierarchical optimization problem; both follow the idea of replacing the underlying optimal control problem by its optimality conditions. The first approach is based on Pontryagin's maximum principle, whereas the second approach uses direct multiple shooting and the corresponding Karush-Kuhn-Tucker conditions. Both approaches pose numerical challenges that are discussed in this paper. Finally, we investigate the performance of our methods by means of a benchmark problem.