Mean field linear-quadratic control: uniform stabilization and social optimality. (English) Zbl 1448.91028
Summary: This paper is concerned with uniform stabilization and social optimality for general mean field linear-quadratic control systems, where subsystems are coupled via individual dynamics and costs, and the state weight is not assumed with the definiteness condition. For the finite-horizon problem, we first obtain a set of forward-backward stochastic differential equations (FBSDEs) from variational analysis, and construct a feedback-type control by decoupling the FBSDEs. For the infinite-horizon problem, by using solutions to two Riccati equations, we design a set of decentralized control laws, which is further proved to be asymptotically social optimal. Some equivalent conditions are given for uniform stabilization of the systems in different cases, respectively. Finally, the proposed decentralized controls are compared to the asymptotic optimal strategies in previous works.
MSC:
| 91A16 | Mean field games (aspects of game theory) |
| 49N10 | Linear-quadratic optimal control problems |
| 49N80 | Mean field games and control |
| 93A16 | Multi-agent systems |
| 93D05 | Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory |
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
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