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Mean-Field Linear-Quadratic-Gaussian (LQG) Games for Stochastic Integral Systems
- Source :
- IEEE Transactions on Automatic Control. 61:2670-2675
- Publication Year :
- 2016
- Publisher :
- Institute of Electrical and Electronics Engineers (IEEE), 2016.
-
Abstract
- In this technical note, we formulate and investigate a class of mean-field linear-quadratic-Gaussian (LQG) games for stochastic integral systems. Unlike other literature on mean-field games where the individual states follow the controlled stochastic differential equations (SDEs), the individual states in our large-population system are characterized by a class of stochastic Volterra-type integral equations. We obtain the Nash certainty equivalence (NCE) equation and hence derive the set of associated decentralized strategies. The $\epsilon$ -Nash equilibrium properties are also verified. Due to the intrinsic integral structure, the techniques and estimates applied here are significantly different from those existing results in mean-field LQG games for stochastic differential systems. For example, some Fredholm equation in the mean-field setup is introduced for the first time. As for applications, two types of stochastic delayed systems are formulated as the special cases of our stochastic integral system, and relevant mean-field LQG games are discussed.
- Subjects :
- Stratonovich integral
0209 industrial biotechnology
Continuous-time stochastic process
Mathematical optimization
010102 general mathematics
Stochastic calculus
02 engineering and technology
01 natural sciences
Integral equation
Computer Science Applications
Stochastic partial differential equation
Stochastic differential equation
020901 industrial engineering & automation
Quantum stochastic calculus
Control and Systems Engineering
Applied mathematics
Optimal projection equations
0101 mathematics
Electrical and Electronic Engineering
Mathematics
Subjects
Details
- ISSN :
- 15582523 and 00189286
- Volume :
- 61
- Database :
- OpenAIRE
- Journal :
- IEEE Transactions on Automatic Control
- Accession number :
- edsair.doi...........05865c780b6ed2ff656e781d36e6f2c8
- Full Text :
- https://doi.org/10.1109/tac.2015.2506620