Exact Set-valued Estimation using Constrained Convex Generators for uncertain Linear Systems

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Abstract

Set-valued state estimation when in the presence of uncertainties in the model have been addressed in the literature essentially following three main approaches: i) interval arithmetic of the uncertain dynamics with the estimates; ii) factorizing the uncertainty into matrices with unity rank; and, iii) performing the convex hull for the vertices of the uncertainty space. Approach i) and ii) introduce a lot of conservatism because both disregard the relationship of the parameters with the entries of the dynamics matrix. On the other hand, approach iii) has a large growth on the number of variables required to represent the set or is approximated losing its main advantage in comparison with i) and ii). In this paper, with the application of autonomous vehicles in GPS-denied areas that resort to beacon signals for localization, we develop an exact (meaning no added conservatism) and optimal (smallest growth in the number of variables) closed-form definition for the convex hull of Convex Constrained Generators (CCGs). This results in a more efficient method to represent the minimum volume convex set corresponding to the state estimation. Given that reductions methods are still lacking in the literature for CCGs, we employ an approximation using ray-shooting that is comparable in terms of accuracy with methods for Constrained Zonotopes as the ones implemented in CORA. Simulations illustrate the greater accuracy of CCGs with the proposed convex hull operation in comparison to Constrained Zonotopes.
Original languageEnglish
Title of host publicationInternational Federation of Automatic Control
Subtitle of host publication22nd IFAC World Congress, Yokohama, Japan, July 9-14, 2023
EditorsHideaki Ishii, Yoshio Ebihara, Jun-ichi Imura, Masaki Yamakita
PublisherElsevier B.V.
Pages9461-9466
Number of pages6
Edition2
ISBN (Print)978-171387234-4
DOIs
Publication statusPublished - 22 Nov 2023
Event22nd IFAC World Congress - Yokohama, Japan
Duration: 9 Jul 202314 Jul 2023

Publication series

NameIFAC-PapersOnLine
PublisherElsevier B.V.
Number2
Volume56
ISSN (Print)2405-8963

Conference

Conference22nd IFAC World Congress
Country/TerritoryJapan
CityYokohama
Period9/07/2314/07/23

Keywords

  • control
  • Guidance navigation
  • Observers for linear systems
  • Parameter-varying systems

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