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Differential Games for Weakly Coupled Large-Scale Linear Stochastic Systems with an H∞-Constraint

Author

Listed:
  • Hiroaki Mukaidani

    (Academy of Hiroshima University, Division of Science and Technology, Informatics Unit, Appointment)

  • Hua Xu

    (Graduate School of Business Sciences, The University of Tsukuba, 3-29-1, Otsuka, Bunkyo-ku, Tokyo, 112-0012, Japan)

Abstract

A differential game approach for the finite-horizon stochastic control problem with an H∞-constraint is considered for a class of large-scale linear systems. First, necessary conditions for the existence of a control strategy set are established by means of cross-coupled stochastic Riccati differential equations (CSRDEs). Second, an efficient design method to obtain a reduced-order parameter-independent approximate strategy set is proposed. Moreover, the performance degradation is estimated. Infinite-horizon case is also discussed. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed design scheme.

Suggested Citation

  • Hiroaki Mukaidani & Hua Xu, 2018. "Differential Games for Weakly Coupled Large-Scale Linear Stochastic Systems with an H∞-Constraint," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 20(01), pages 1-24, March.
    • Handle: RePEc:wsi:igtrxx:v:20:y:2018:i:01:n:s0219198917500256
    DOI: 10.1142/S0219198917500256
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