# 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 ...

## 25 Citations

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## References

SHOWING 1-10 OF 62 REFERENCES

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

- Mathematics52nd IEEE Conference on Decision and Control
- 2013

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

- Mathematics1982 American Control Conference
- 1982

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

- Mathematics52nd IEEE Conference on Decision and Control
- 2013

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

- MathematicsSIAM J. Control. Optim.
- 2012

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

- MathematicsSIAM 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

- Geology
- 2013

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

- MathematicsNetworks 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

- MathematicsSIAM J. Control. Optim.
- 2002

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

- Economics
- 2002

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

- MathematicsIEEE Transactions on Automatic Control
- 2014

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.