A robust optimal control problem with moment constraints on distribution: Theoretical analysis and an algorithm

IF 4.1 2区 工程技术 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Computers & Operations Research Pub Date : 2024-12-30 DOI:10.1016/j.cor.2024.106966
Jianxiong Ye , Lei Wang , Changzhi Wu , Jie Sun , Kok Lay Teo , Xiangyu Wang
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Abstract

We study an optimal control problem in which both the objective function and the dynamic constraint contain an uncertain parameter. Since the distribution of this uncertain parameter is not exactly known, the objective function is taken as the worst-case expectation over a set of possible distributions of the uncertain parameter. This ambiguity set of distributions is, in turn, defined by the first two moments of the random variables involved. The optimal control is found by minimizing the worst-case expectation over all possible distributions in this set. If the distributions are discrete, the stochastic minimax optimal control problem can be converted into a conventional optimal control problem via duality, which is then approximated as a finite-dimensional optimization problem via the control parametrization. We derive necessary conditions of optimality and propose an algorithm to solve the approximation optimization problem. The results of discrete probability distribution are then extended to the case with one dimensional continuous stochastic variable by applying the control parametrization methodology on the continuous stochastic variable, and the convergence results are derived. A numerical example is present to illustrate the potential application of the proposed model and the effectiveness of the algorithm.
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来源期刊
Computers & Operations Research
Computers & Operations Research 工程技术-工程:工业
CiteScore
8.60
自引率
8.70%
发文量
292
审稿时长
8.5 months
期刊介绍: Operations research and computers meet in a large number of scientific fields, many of which are of vital current concern to our troubled society. These include, among others, ecology, transportation, safety, reliability, urban planning, economics, inventory control, investment strategy and logistics (including reverse logistics). Computers & Operations Research provides an international forum for the application of computers and operations research techniques to problems in these and related fields.
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