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Minimum-Radius Criterion for a Zonotopic State Estimator based on Degrees of Freedom
  • Alesi Augusto de Paula,
  • Guilherme Raffo,
  • Bruno Teixeira
Alesi Augusto de Paula
Universidade Federal de Minas Gerais

Corresponding Author:[email protected]

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Guilherme Raffo
Universidade Federal de Minas Gerais
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Bruno Teixeira
Universidade Federal de Minas Gerais
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This paper proposes a new cost criterion to enhance the precision of a zonotopic state estimator for discrete-time descriptor linear systems. Originally, the algorithm solves a minimum-trace problem involving zonotopes, whose evolution is given by an interval observer structure containing extra design matrices, called degrees of freedom. Although the minimization of trace yields explicit solutions, it does not necessarily imply minimization of volume, and thereby, the precision of the output zonotope cannot be improved effectively. The volume measure for zonotopes is computationally expensive and, when used as cost criterion, implies nonlinear optimization problems. Motivated by such issues, we here propose a minimum-radius criterion where the smallest box enclosing the output zonotope is minimized. The resulting optimization problem is nonlinear, but its convexity is exploited to yield an equivalent linear program. The effectiveness of our approach is illustrated over two numerical examples.
13 Jan 2023Submitted to Optimal Control, Applications and Methods
14 Jan 2023Assigned to Editor
14 Jan 2023Review(s) Completed, Editorial Evaluation Pending
14 Jan 2023Submission Checks Completed
28 Feb 2023Reviewer(s) Assigned
01 May 2023Editorial Decision: Revise Minor
27 Oct 20231st Revision Received
31 Oct 2023Assigned to Editor
31 Oct 2023Submission Checks Completed
31 Oct 2023Review(s) Completed, Editorial Evaluation Pending