Solution to Mixed H2/H Control for Discrete–time Systems with (x,u,v)–dependent Noise

  • Xiaoqian Li
  • Wei WangEmail author
  • Juanjuan Xu
  • Huanshui Zhang
Regular Papers Control Theory and Applications


In this paper, the stochastic H2/H control problem for linear discrete–time systems with (x,u,v)–dependent noise is studied. By applying the leader–follower stochastic game approach, the disturbance is treated as the follower and the control input is treated as the leader, respectively. Necessary and sufficient conditions for the mixed control problem are presented which guarantee the existence and uniqueness of the optimal solution. By applying the stochastic maximum principle, the follower first solves a stochastic linear quadratic optimal control problem which is given in the form of H–norm with the aid of stochastic Riccati equations. Then the leader solves a stochastic linear quadratic problem with the aid of forward and backward equations. The main technique is to introduce two new co–states to capture the future information, the encountered difficulty is to establish a homogeneous relationship between the new co–states.


Leader–follower game approach necessary and sufficient conditions Riccati equation stochastic H2/H control 


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Copyright information

© Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Xiaoqian Li
    • 1
  • Wei Wang
    • 1
    Email author
  • Juanjuan Xu
    • 1
  • Huanshui Zhang
    • 1
  1. 1.School of Control Science and EngineeringShandong UniversityJinanP. R. China

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