Robust Mean Field Linear-Quadratic-Gaussian Games with Unknown L2-Disturbance

@article{Huang2017RobustMF,
  title={Robust Mean Field Linear-Quadratic-Gaussian Games with Unknown L2-Disturbance},
  author={Jianhui Huang and Minyi Huang},
  journal={SIAM J. Control. Optim.},
  year={2017},
  volume={55},
  pages={2811-2840}
}
This paper considers a class of mean field linear-quadratic-Gaussian games with model uncertainty. The drift term in the dynamics of the agents contains a common unknown function. We take a robust ... 
View PDF on arXiv
25 Citations
Highly Influential Citations
2
Background Citations
11
Methods Citations
3
Results Citations
1

25 Citations

Social Optima in Mean Field Linear-Quadratic-Gaussian Control with Volatility Uncertainty

This paper examines mean field linear-quadratic-Gaussian social optimum control with volatility-uncertain common noise and applies a robust optimization approach in which all agents view volatility uncertainty as an adversarial player.

Social optima in linear quadratic mean field control with unmodeled dynamics and multiplicative noise

This paper investigates the linear‐quadratic social control problem for mean field systems with unmodeled dynamics and multiplicative noise. The objective of each agent is to optimize the social cost…

Robust linear quadratic mean field social control: A direct approach

This paper investigates a robust linear quadratic mean field team control problem. The model involves a global uncertainty drift which is common for a large number of weakly-coupled interactive…

Social Optima in Mean Field LQ Control with Local Disturbance

This paper first considers the centralized strategies using personby-person optimality and then constructs an auxiliary optimal control problem with mean field approximation, which design the decentralized strategies, which are shown to have asymptotic robust social optimality.

Linear Quadratic Mean Field Games: Decentralized O(1/N)-Nash Equilibria

This paper studies an asymptotic solvability problem for linear quadratic (LQ) mean field games with controlled diffusions and indefinite weights for the state and control in the costs. The authors…

Robust Time-Inconsistent Stochastic Linear-Quadratic Control with Drift Disturbance

This paper studies stochastic linear-quadratic control with a time-inconsistent objective and worst-case drift disturbance. We allow the agent to introduce disturbances to reflect her uncertainty…

Decentralized strategies for finite population linear-quadratic-Gaussian games and teams

A Unified Relation Analysis of Linear-quadratic Mean-field Game, Team and Control

—This paper revisits well-studied dynamic decisions of weakly coupled large-population (LP) systems. Specifically, three types of LP decision problems: mean-field game (MG), mean- field team (MT), and…

Linear Quadratic Gaussian Mean-Field Controls of Social Optima

This paper investigates a class of unified stochastic linear-quadratic-Gaussian (LQG) social optima problems involving a large number of weakly-coupled interactive agents under a generalized setting and derives a decentralized social control derived by aclass of new type consistency condition (CC) system for typical representative agent.

Robust Time-Inconsistent Stochastic Linear-Quadratic Control

This paper studies stochastic linear-quadratic control problems for an ambiguity-adverse agent with a time-inconsistent objective. We allow the agent to incorporate disturbances into the state's…

References

SHOWING 1-10 OF 62 REFERENCES

Robust linear quadratic mean-field games in crowd-seeking social networks

A robust mean-field game model in the spirit of H∞-optimal control is provided, existence of a mean- field equilibrium is established, and its stochastic stability is analyzed.

Minimax Control of Linear Stochastic Systems with Noise Uncertainty

The linear-quadratic-Gaussian regulator problem is considered for multivariable linear stochastic systems with uncertain second-order statistical properties. Uncertainty is modeled by allowing…

Mean field LQG games with model uncertainty

This paper considers a class of mean field linear-quadratic-Gaussian (MFLQG) games and deals with the model uncertainty by a robust optimization approach and formulate a minimax control problem in the infinite population limit.

Linear-Quadratic-Gaussian Mixed Games with Continuum-Parametrized Minor Players

A mean field linear-quadratic-Gaussian game with a major player and a large number of minor players parametrized by a continuum set has an $\varepsilon$-Nash equilibrium property when applied to the large but finite population model.

Linear-Quadratic Optimal Control Problems for Mean-Field Stochastic Differential Equations

  • J. Yong
  • Mathematics
    SIAM J. Control. Optim.
  • 2013
Linear-quadratic optimal control problems are considered for mean-field stochastic differential equations with deterministic coefficients using a variational method and two Riccati differential equations are obtained which are uniquely solvable under certain conditions.

Mean Field Games and Mean Field Type Control Theory

Introduction.- General Presentation of Mean Field Control Problems.- Discussion of the Mean Field game.- Discussion of the Mean Field Type Control.- Approximation of Nash Games with a large number of…

Explicit solutions of some linear-quadratic mean field games

  • M. Bardi
  • Mathematics
    Networks Heterog. Media
  • 2012
The quadratic-Gaussian solution to a system of two differential equations of the kind introduced by Lasry and Lions in the theory of Mean Field Games is solved and the L-Q model is compared with other Mean Field models of population distribution.

Minimax LQG Control of Stochastic Partially Observed Uncertain Systems

A minimax optimal LQG controller is constructed which is based on a pair of algebraic matrix Riccati equations arising in risk-sensitive control and absolutely stabilizes the stochastic uncertain system.

Robust Equilibria in Indefinite Linear-Quadratic Differential Games

Equilibria in dynamic games are formulated often under the assumption that the players have full knowledge of the dynamics to which they are subject. Here, we formulate equilibria in which players…

Risk-Sensitive Mean-Field Games

It is shown that under appropriate regularity conditions, the mean-field value of the stochastic differential game with exponentiated integral cost functional coincides with the value function satisfying a Hamilton -Jacobi- Bellman (HJB) equation with an additional quadratic term.
...