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Social Optima in Linear Quadratic Mean Field Control with Heterogeneous Agents
Asian Control Conference, 2022This paper studies a class of heterogeneous linear quadratic mean field team (LQ-MFT) control problems. We reform the original direct approach and tackle the problem by ascending the dimension of the LQ-MFT system according to the number of categories ...
Tinghan Xie, Bing‐Chang Wang
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IEEE Conference on Decision and Control, 2021
We consider linear quadratic (LQ) Stackelberg games with a major player (leader) and N minor players (followers) and derive two master equations in a mean field limit model. We show the resulting decentralized strategies are time consistent by adapting a
Xuwei Yang, Minyi Huang
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We consider linear quadratic (LQ) Stackelberg games with a major player (leader) and N minor players (followers) and derive two master equations in a mean field limit model. We show the resulting decentralized strategies are time consistent by adapting a
Xuwei Yang, Minyi Huang
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Linear Quadratic Mean Field Social Optimization: Asymptotic Solvability and Decentralized Control
Applied Mathematics and Optimization, 2020This paper studies asymptotic solvability of a linear quadratic mean field social optimization problem with controlled diffusions and indefinite state and control weights.
Minyi Huang, Xuwei Yang
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Linear quadratic mean field Stackelberg differential games
Automatica, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jun Moon, T. Başar
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An Open-Loop Stackelberg Strategy for the Linear Quadratic Mean-Field Stochastic Differential Game
IEEE Transactions on Automatic Control, 2019This paper is concerned with the open-loop linear–quadratic (LQ) Stackelberg game of the mean-field stochastic systems in finite horizon. By means of two generalized differential Riccati equations, the follower first solves a mean-field stochastic LQ ...
Yaning Lin, Xiushan Jiang, Weihai Zhang
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IEEE Transactions on Automatic Control
The linear–quadratic mean field social control problem is studied in a large-population system with heterogeneous agents following the direct approach.
Yong Liang, Bing-Chang Wang, Huan Zhang
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The linear–quadratic mean field social control problem is studied in a large-population system with heterogeneous agents following the direct approach.
Yong Liang, Bing-Chang Wang, Huan Zhang
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Linear–Quadratic Time-Inconsistent Mean Field Games
Dynamic Games and Applications, 2013zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Bensoussan, A. +2 more
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Cramér-type conditions and quadratic mean differentiability
Annals of the Institute of Statistical Mathematics, 1977Let (Ω,A) be a measurable space, let Θ be an open set inR k , and let {P θ; θ∈Θ} be a family of probability measures defined onA. Let μ be a σ-finite measure onA, and assume thatP θ≪μ for each θ∈Θ. Let us denote a specified version ofdP θ /d μ byf(ω; θ).
Lind, Bruce, Roussas, George
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Operator means and matrix quadratic equations
Linear Algebra and its Applications, 2021zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Meaning of quadratic structure functions
Journal of the Optical Society of America, 1980Quadratic structure functions are sometimes used to describe the phase of partially coherent waves. The physical significance of such structure functions, that they describe a tilted but unwarped phase, limits their applicability to propagation calculations.
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