Guaranteed State Estimation via Direct Polytopic Set Computation for Nonlinear Discrete-Time Systems

Mohammad Khajenejad, Fatima Shoaib, Sze Zheng Yong

Research output: Contribution to journalArticlepeer-review

Abstract

This letter introduces a set-theoretic state estimation approach for bounded-error nonlinear discrete-time systems, subject to nonlinear observations or constraints, when polytope-valued uncertainties are assumed. Our approach relies on finding a polytopic enclosure to the true range of nonlinear mappings via the direct use of hyperplane and vertex representations of polytopes. In particular, we derive a tractable enclosure of the set-product of an interval and a polytope, which is then used in a two-step state estimation approach consisting of (i) state propagation (prediction) using the nonlinear system dynamics and (ii) measurement update (refinement) based on nonlinear observations. Moreover, we analyze the computational complexity of our proposed technique and derive sufficient conditions for stability of the estimation errors. Finally, we compare the effectiveness of our approach with existing polytopic and interval observers in the literature.

Original languageEnglish (US)
Pages (from-to)2060-2065
Number of pages6
JournalIEEE Control Systems Letters
Volume6
DOIs
StatePublished - 2022
Externally publishedYes

Keywords

  • Estimation
  • observers for nonlinear systems
  • polytope-valued observers
  • uncertain systems

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Control and Optimization

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