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Robust SOF Stackelberg game for stochastic LPV systems

  • Research Paper
  • Special Focus on Control and Analysis for Stochastic Systems
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Abstract

A robust static output feedback (SOF) Stackelberg game with multiple followers in stochastic linear parameter varying (LPV) systems is investigated. The conditions for the existence of a robust SOF Stackelberg strategy set under H∞ constraints are established by the cross-coupled matrix inequality (CCMI). To determine this strategy set, the optimization problems corresponding to the relevant cost bounds are defined, and their solution sets are derived using the Karush-Kuhn-Tucker conditions. The results show that the robust SOF Stackelberg strategy set can be obtained by solving higher-order cross-coupled matrix equations (CCMEs). Because CCMEs are complex and difficult to solve numerically, a heuristic algorithm is developed by combining the CCMEs with the CCMIs. The convergence property is proven using the Krasnoselskii-Mann (KM) iteration algorithm. Finally, two numerical examples are solved to demonstrate the reliability and usefulness of the proposed heuristic algorithm.

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Authors and Affiliations

  1. Graduate School of Advanced Science and Engineering, Hiroshima University, Higashi-Hiroshima, 739-8527, Japan

    Hiroaki Mukaidani

  2. Faculty of Business Sciences, The University of Tsukuba, Tokyo, 112-0012, Japan

    Hua Xu

Authors
  1. Hiroaki Mukaidani
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  2. Hua Xu
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Correspondence to Hiroaki Mukaidani.

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Mukaidani, H., Xu, H. Robust SOF Stackelberg game for stochastic LPV systems. Sci. China Inf. Sci. 64, 200202 (2021). https://doi.org/10.1007/s11432-021-3302-5

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  • DOI: https://doi.org/10.1007/s11432-021-3302-5

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