给定参考轨迹的奇摄动最优跟踪问题的分解

IF 0.58 Q3 Engineering

Journal of Applied and Industrial Mathematics Pub Date : 2023-11-04 DOI:10.1134/S1990478923030171

V. A. Sobolev

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引用次数: 0

摘要

首次考虑了奇异摄动下给定参考轨迹和积分二次型性能准则的最优跟踪问题。利用分解方法分析了求解该问题时产生的奇摄动微分系统。该方法基于快速和慢速运动的积分流形技术。构造了次优控制，使用该次优控制会导致最优和次优控制的最小化泛函的值相差表征奇异扰动的小参数的二次幂的理论量。

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Decomposition of Singularly Perturbed Optimal Tracking Problems with a Given Reference Trajectory

For the first time, the problem of optimal tracking with a given reference trajectory and an integral quadratic performance criterion in the presence of singular perturbations is considered. The decomposition method is used to analyze singularly perturbed differential systems that arise in solving this problem. The method is based on the technique of integral manifolds of fast and slow motions. A suboptimal control is constructed the use of which leads to a difference in the values of the minimized functional for the optimal and suboptimal controls by an amount of the order of the second power of a small parameter characterizing singular perturbations.

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来源期刊

Journal of Applied and Industrial Mathematics Engineering-Industrial and Manufacturing Engineering

CiteScore

1.00

自引率

0.00%

发文量

期刊介绍： Journal of Applied and Industrial Mathematics is a journal that publishes original and review articles containing theoretical results and those of interest for applications in various branches of industry. The journal topics include the qualitative theory of differential equations in application to mechanics, physics, chemistry, biology, technical and natural processes; mathematical modeling in mechanics, physics, engineering, chemistry, biology, ecology, medicine, etc.; control theory; discrete optimization; discrete structures and extremum problems; combinatorics; control and reliability of discrete circuits; mathematical programming; mathematical models and methods for making optimal decisions; models of theory of scheduling, location and replacement of equipment; modeling the control processes; development and analysis of algorithms; synthesis and complexity of control systems; automata theory; graph theory; game theory and its applications; coding theory; scheduling theory; and theory of circuits.