Asynchronous quadratic control for constrained hidden markov jump linear systems with incomplete MTPM and MOCPM

Jin Zhu, Kai Xia, Geir E. Dullerud

Research output: Contribution to journalArticlepeer-review

Abstract

This paper investigates the quadratic optimal control problem for constrained Markov jump linear systems with incomplete mode transition probability matrix (MTPM). Considering original system mode is not accessible, observed mode is utilized for asynchronous controller design where mode observation conditional probability matrix (MOCPM), which characterizes the emission between original modes and observed modes is assumed to be partially known. An LMI optimization problem is formulated for such constrained hidden Markov jump linear systems with incomplete MTPM and MOCPM. Based on this, a feasible state-feedback controller can be designed with the application of free-connection weighting matrix method. The desired controller, dependent on observed mode, is an asynchronous one which can minimize the upper bound of quadratic cost and satisfy restrictions on system states and control variables. Furthermore, clustering observation where observed modes recast into several clusters, is explored for simplifying the computational complexity. Numerical examples are provided to illustrate the validity.

Original languageEnglish (US)
Pages (from-to)714-742
Number of pages29
JournalIMA Journal of Mathematical Control and Information
Volume38
Issue number2
DOIs
StatePublished - Jun 1 2021

Keywords

  • asynchronous quadratic control
  • cluster observation
  • Constrained hidden Markov jump linear systems
  • incomplete MTPM and MOCPM

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Control and Optimization
  • Applied Mathematics

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