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

Hiroaki Mukaidani () and Hua Xu ()
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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

International Game Theory Review (IGTR), 2018, vol. 20, issue 01, 1-24

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.

Keywords: Robust differential game; stochastic large-scale systems; cross-coupled stochastic Riccati differential equations (CSRDEs); H∞-constraint (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1142/S0219198917500256

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