仿射问题中 Bang-Bang 控制的稳定性和通用性

IF 2.2 2区数学 Q2 AUTOMATION & CONTROL SYSTEMS

SIAM Journal on Control and Optimization Pub Date : 2024-06-11 DOI:10.1137/23m1586446

Alberto Domínguez Corella, Gerd Wachsmuth

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引用次数: 0

摘要

SIAM 控制与优化期刊》第 62 卷第 3 期第 1669-1689 页，2024 年 6 月。摘要我们分析了仿射最优控制问题中 bang-bang 特性的作用。我们证明，仿射问题的许多基本稳定性只有在最小化子为砰砰时才能满足。我们利用 Stegall 变分原理证明，几乎任何线性扰动都会导致砰砰严格全局最小化。我们举例说明了我们的结果在特定最优控制问题中的适用性。

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Stability and Genericity of Bang-Bang Controls in Affine Problems

SIAM Journal on Control and Optimization, Volume 62, Issue 3, Page 1669-1689, June 2024.
Abstract. We analyze the role of the bang-bang property in affine optimal control problems. We show that many essential stability properties of affine problems are only satisfied when minimizers are bang-bang. We employ Stegall’s variational principle to prove that almost any linear perturbation leads to a bang-bang strict global minimizer. Examples are given to show the applicability of our results to specific optimal control problems.

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来源期刊

SIAM Journal on Control and Optimization 数学-应用数学

CiteScore

4.00

自引率

4.50%

发文量

143

审稿时长

12 months

期刊介绍： SIAM Journal on Control and Optimization (SICON) publishes original research articles on the mathematics and applications of control theory and certain parts of optimization theory. Papers considered for publication must be significant at both the mathematical level and the level of applications or potential applications. Papers containing mostly routine mathematics or those with no discernible connection to control and systems theory or optimization will not be considered for publication. From time to time, the journal will also publish authoritative surveys of important subject areas in control theory and optimization whose level of maturity permits a clear and unified exposition. The broad areas mentioned above are intended to encompass a wide range of mathematical techniques and scientific, engineering, economic, and industrial applications. These include stochastic and deterministic methods in control, estimation, and identification of systems; modeling and realization of complex control systems; the numerical analysis and related computational methodology of control processes and allied issues; and the development of mathematical theories and techniques that give new insights into old problems or provide the basis for further progress in control theory and optimization. Within the field of optimization, the journal focuses on the parts that are relevant to dynamic and control systems. Contributions to numerical methodology are also welcome in accordance with these aims, especially as related to large-scale problems and decomposition as well as to fundamental questions of convergence and approximation.