Multiplayer Noncooperative and Cooperative Minimax H∞ Tracking Game Strategies for Linear Mean-Field Stochastic Systems With Applications to Cyber-Social Systems

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Abstract
The multiplayer stochastic noncooperative tracking game (NTG) with conflicting target strategy and cooperative tracking game (CTG) with a common target strategy of the mean-field stochastic jump-diffusion (MFSJD) system with external disturbance is investigated in this study. Due to the mean (collective) behavior in the system dynamic and cost function, the designs of the NTG strategy and CTG strategy for target tracking of the MFSJD system are more difficult than the conventional stochastic system. By the proposed indirect method, the NTG and CTG strategy design problems are transformed into linear matrix inequalities (LMIs)-constrained multiobjective optimization problem (MOP) and LMIs-constrained single-objective optimization problem (SOP), respectively. The LMIs-constrained MOP could be solved effectively for all Nash equilibrium solutions of NTG at the Pareto front by the proposed LMIs-constrained multiobjective evolutionary algorithm (MOEA). Two simulation examples, including the share market allocation and network security strategies in cyber-social systems, are given to illustrate the design procedure and validate the effectiveness of the proposed LMI-constrained MOEA for all Nash equilibrium solutions of NTG strategies of the MFSJD system.
Funding Information
  • Ministry of Science and Technology of Taiwan (MOST 108-2221-E-007-099-MY3)

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