Interpopulation and Intrapopulation Linear Quadratic Differential Games

IF 5 3区计算机科学 Q2 AUTOMATION & CONTROL SYSTEMS

IEEE Transactions on Control of Network Systems Pub Date : 2025-02-04 DOI:10.1109/TCNS.2025.3538459

Julian Barreiro-Gomez

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引用次数: 0

Abstract

We studymultipopulation game problems consisting of both interpopulation and intrapopulation strategic interactions. In the proposed model, the intrapopulation dynamics is given by a stochastic differential equation (SDE) and the strategic interaction occurs among agents who are homogeneous within the same population. A stochastic aggregative game takes place in the intrapopulation game problem. The interpopulation dynamics is given by the aggregative behavior of each population and an ordinary differential equation (ODE). The other strategic interaction occurs among different heterogeneous populations in either a noncooperative or cooperative way. In addition, the interaction for the different populations is performed in a distributed manner over a graph that might also be considered time-varying. We provideconditions to compute the solution by means of dynamic programming, and providesemi-explicit solutions for the linear-quadratic case by solving the emerging Hamilton–Jacobi–Bellman partial differential equation (PDE) and postulating an appropriate ansatz for the value functional. A numerical example illustrates the presented results.

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种群间和种群内线性二次微分对策

我们研究由种群间和种群内策略相互作用组成的多种群博弈问题。在该模型中，种群内动力学由随机微分方程（SDE）给出，策略相互作用发生在同一种群内同质个体之间。在种群内博弈问题中存在随机聚集博弈。种群间动力学由各种群的聚集行为和常微分方程给出。另一种战略互动发生在不同的异质群体之间，以非合作或合作的方式进行。此外，不同种群的相互作用以分布方式在可能也被认为是时变的图上执行。通过求解新出现的Hamilton-Jacobi-Bellman偏微分方程（PDE），并假设值泛函的适当方差，给出了线性二次情形的半显式解。数值算例说明了所得结果。

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

IEEE Transactions on Control of Network Systems Mathematics-Control and Optimization

CiteScore

7.80

自引率

7.10%

发文量

169

期刊介绍： The IEEE Transactions on Control of Network Systems is committed to the timely publication of high-impact papers at the intersection of control systems and network science. In particular, the journal addresses research on the analysis, design and implementation of networked control systems, as well as control over networks. Relevant work includes the full spectrum from basic research on control systems to the design of engineering solutions for automatic control of, and over, networks. The topics covered by this journal include: Coordinated control and estimation over networks, Control and computation over sensor networks, Control under communication constraints, Control and performance analysis issues that arise in the dynamics of networks used in application areas such as communications, computers, transportation, manufacturing, Web ranking and aggregation, social networks, biology, power systems, economics, Synchronization of activities across a controlled network, Stability analysis of controlled networks, Analysis of networks as hybrid dynamical systems.