期刊
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
卷 68, 期 7, 页码 4113-4126出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TAC.2022.3202824
关键词
Cooperative games; ye-representation ap-proach; mean-field theory; Pareto optimality; stochastic linear-quadratic (LQ) optimal control
This article investigates a mean-field stochastic cooperative linear-quadratic dynamic difference game in an infinite time horizon. It derives the necessary and sufficient conditions for stability, observability, and detectability of mean-field stochastic linear difference systems. The article also characterizes the solvability of cross-coupled generalized Lyapunov equations and the uniqueness of positive-definite solutions. Furthermore, it presents a practical application on computation offloading in multiaccess edge computing network to illustrate the proposed theoretical results.
This article is concerned with the mean-field stochastic cooperative linear-quadratic dynamic difference game in an infinite time horizon. First, the necessary and sufficient conditions for the stability in the mean-square sense and the stochastic Popov-Belevitch-Hautus eigenvector tests for the exact observability and exact detectability of mean-field stochastic linear difference systems are derived by the $\mathscr H-representation technique. Second, the relation between the solvability of the cross-coupled generalized Lyapunov equations and the exact observability, exact detectability, and stability of the mean-field dynamic system is well characterized. It is then shown that the cross-coupled algebraic Riccati equations (CC-AREs) admit a unique positive-definite (positive-semidefinite, respectively) solution under exact observability (exact detectability, respectively), which is also a feedback stabilizing solution. Furthermore, all the Pareto optimal strategies and solutions can be, respectively, derived via the solutions to the weighted CC-AREs and the weighted cross-coupled algebraic Lyapunov equations. Finally, a practical application on the computation offloading in the multiaccess edge computing network is presented to illustrate the proposed theoretical results.
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