Exact Controllability for Mean-Field Type Linear Game-Based Control Systems

IF 1.6 2区数学 Q2 MATHEMATICS, APPLIED

Applied Mathematics and Optimization Pub Date : 2024-05-30 DOI:10.1007/s00245-024-10149-y

Cui Chen, Zhiyong Yu

引用次数: 0

Abstract

Motivated by the self-pursuit of controlled objects, we consider the exact controllability of a linear mean-field type game-based control system (MF-GBCS, for short) generated by a linear-quadratic (LQ, for short) Nash game. A Gram-type criterion for the general time-varying coefficients case and a Kalman-type criterion for the special time-invariant coefficients case are obtained. At the same time, the equivalence between the exact controllability of this MF-GBCS and the exact observability of a dual system is established. Moreover, an admissible control that can steer the state from any initial vector to any terminal random variable is constructed in closed form.

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平均场型线性博弈控制系统的精确可控性

受受控对象自我追求的启发，我们考虑了由线性-二次方（简称 LQ）纳什博弈产生的线性均场型博弈控制系统（简称 MF-GBCS）的精确可控性。结果得到了一般时变系数情况下的格拉姆型判据和特殊时变系数情况下的卡尔曼型判据。同时，还建立了该 MF-GBCS 的精确可控性与对偶系统的精确可观测性之间的等价关系。此外，还以闭合形式构建了可将状态从任意初始向量引导至任意终端随机变量的容许控制。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Applied Mathematics and Optimization 数学-应用数学

CiteScore

3.30

自引率

5.60%

发文量

103

审稿时长

>12 weeks

期刊介绍： The Applied Mathematics and Optimization Journal covers a broad range of mathematical methods in particular those that bridge with optimization and have some connection with applications. Core topics include calculus of variations, partial differential equations, stochastic control, optimization of deterministic or stochastic systems in discrete or continuous time, homogenization, control theory, mean field games, dynamic games and optimal transport. Algorithmic, data analytic, machine learning and numerical methods which support the modeling and analysis of optimization problems are encouraged. Of great interest are papers which show some novel idea in either the theory or model which include some connection with potential applications in science and engineering.