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    N-Player Statistical Nash Game Control: M-th Cost Cumulant Optimization

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    Genre
    Thesis/Dissertation
    Date
    2014
    Author
    Aduba, Chukwuemeka Nnabuife
    Advisor
    Won, Chang-Hee, 1967-
    Committee member
    Helferty, John J.
    Hutapea, Parsaoran
    Ferrese, Frank
    Du, Xiaojiang
    Department
    Electrical and Computer Engineering
    Subject
    Electrical Engineering
    Applied Mathematics
    Statistics
    Cumulant Control
    Game Theory
    Nash Game
    Nonlinear Systems
    Statistical Optimal Control
    Stochastic Control
    Permanent link to this record
    http://hdl.handle.net/20.500.12613/2529
    
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    DOI
    http://dx.doi.org/10.34944/dspace/2511
    Abstract
    Game theory is the study of tactical interactions involving conflicts and cooperations among multiple decision makers called players with applications in diverse disciplines such as economics, biology, management, communication networks, electric power systems and control. This dissertation studies a statistical differential game problem where finite N players optimize their system performance by shaping the distribution of their cost function through cost cumulants. This research integrates game theory with statistical optimal control theory and considers a statistical Nash non-cooperative nonzero-sum game for a nonlinear dynamic system with nonquadratic cost functions. The objective of the statistical Nash game is to find the equilibrium solution where no player has the incentive to deviate once other players maintain their equilibrium strategy. The necessary condition for the existence of the Nash equilibrium solution is given for the m-th cumulant cost optimization using the Hamilton-Jacobi-Bellman (HJB) equations. In addition, the sufficient condition which is the verification theorem for the existence of Nash equilibrium solution is given for the m-th cumulant cost optimization using the Hamilton-Jacobi-Bellman (HJB) equations. However, solving the HJB equations even for relatively low dimensional game problem is not trivial, we propose to use neural network approximate method to find the solution of the HJB partial differential equations for the statistical game problem. Convergence proof of the neural network approximate method solution to exact solution is given. In addition, numerical examples are provided for the statistical game to demonstrate the applicability of the proposed theoretical developments.
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