Computation of robust control invariant sets with predefined complexity for uncertain systems

Ankit Gupta*, Hakan Köroğlu, Paolo Falcone

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

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Abstract

This paper presents an algorithm that computes polytopic robust control-invariant (RCI) sets for rationally parameter-dependent systems with additive disturbances. By means of novel linear matrix inequalities (LMI) feasibility conditions for invariance along with a newly developed method for volume maximization, an iterative algorithm is proposed for the computation of RCI sets with maximized volumes. The obtained RCI sets are symmetric around the origin by construction and have a user-defined level of complexity. Unlike many similar approaches, the proposed algorithm directly computes the RCI sets without requiring control inputs to be in a specific feedback form. In fact, a specific control input is obtained from the LMI problem for each extreme point of the RCI set. The outcomes of the proposed algorithm can be used to construct a piecewise-affine controller based on offline computations.

Original languageEnglish
Pages (from-to)1674-1688
Number of pages15
JournalInternational journal of robust and nonlinear control
Volume31
Issue number5
DOIs
Publication statusPublished - 25 Mar 2021

Keywords

  • invariant set
  • linear fractional transformation
  • linear matrix inequalities
  • linear systems
  • semi-definite program

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