State and mode feedback control strategy for discrete-time Markovian jump linear systems with time-varying controllable mode transition probability matrix

Jin Zhu, Xinghua Wu, Chaoxiang Li, Geir E. Dullerud

Research output: Contribution to journalArticlepeer-review

Abstract

In this article, the state and mode feedback control strategy is investigated for the discrete-time Markovian jump linear system (MJLS) with time-varying controllable mode transition probability matrix (MTPM). This strategy, consisting of a state feedback controller and a mode feedback controller, is proposed to ensure MJLS's stability and meanwhile improve system performance. First, a mode-dependent state feedback controller is designed to stabilize the MJLS based on the time-invariant part of the MTPM such that it can still keep valid even if the MTPM is adjusted by the mode feedback control. Second, a generalized quadratic stabilization cost is put forward for evaluating MJLS's performance, which contains system state, state feedback controller, and mode feedback controller. To reduce the stabilization cost, a mode feedback controller is introduced to adjust each mode's occurrence probability by changing the time-varying controllable part of MTPM. The calculation of such mode feedback controller is given based on a value-iteration algorithm with its convergence proof. Compared with traditional state feedback control strategy, this state and mode feedback control strategy offers a new perspective for the control problem of general nonhomogeneous MJLSs. Numerical examples are provided to illustrate the validity of the proposed strategy.

Original languageEnglish (US)
Pages (from-to)3501-3519
Number of pages19
JournalInternational Journal of Robust and Nonlinear Control
Volume30
Issue number8
DOIs
StatePublished - May 25 2020

Keywords

  • Markovian jump linear systems
  • stabilization cost
  • state and mode feedback control strategy
  • time-varying controllable mode transition probability matrix
  • value-iteration algorithm

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Chemical Engineering(all)
  • Biomedical Engineering
  • Aerospace Engineering
  • Mechanical Engineering
  • Industrial and Manufacturing Engineering
  • Electrical and Electronic Engineering

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