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State Estimators for Discrete-Time Descriptor Linear Systems with Mixed Uncertainties and State Constraints
  • Alesi Augusto de Paula,
  • Guilherme Raffo,
  • Bruno Teixeira
Alesi Augusto de Paula
Universidade Federal de Minas Gerais Departamento de Engenharia Eletrica

Corresponding Author:[email protected]

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Guilherme Raffo
Universidade Federal de Minas Gerais Departamento de Engenharia Eletrica
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Bruno Teixeira
Universidade Federal de Minas Gerais Departamento de Engenharia Eletrica
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Abstract

This paper presents two novel mixed-uncertainty state estimators for discrete-time descriptor linear systems, namely linear time-varying mixed-uncertainty filter (LTVMF) and linear time-invariant mixed-uncertainty filter (LTIMF). The former estimator is based on the minimum-variance approach, from which quadratic and explicit formulations are derived and addressed to LTI and LTV systems. Both formulations incorporate the knowledge of state linear constraints, such as equality (in the descriptor form) and inequality, to mitigate precision and accuracy issues related to initialization and evolution of the state estimates. The explicit version is developed to reduce the computational burden of quadratic solvers, which is based on a particularity of the state inequality constraints. The LTIMF algorithm is based on the mixed H 2 / H ∞ criterion motivated by performing low-cost computations. This speed benefit is originated from a reachability analysis involving constant design matrices. Both LTVMF and LTIMF algorithms solve state-estimation problems in which the uncertainties are combined to yield the so-called mixed-uncertainty vector, which is composed by set-bounded uncertainties, characterized by constrained zonotopes, and stochastic uncertainties, characterized by Gaussian random vectors. As mixed-uncertainty vectors imply biobjective optimization problems, we innovatively present multiobjective arguments to justify the choice of the solution on the Pareto-optimal front. According to these arguments, LTVMF is introduced with a cost normalization, which enables the combination of beyond minimum-variance approaches. Likewise, the mixed H 2 / H ∞ criterion of LTIMF is introduced with slack variables to improve the quality of the state estimates. In order to discuss the advantages and drawbacks, the state estimators are tested in two numerical examples.
19 Jun 2023Submitted to International Journal of Robust and Nonlinear Control
19 Jun 2023Assigned to Editor
19 Jun 2023Submission Checks Completed
19 Jun 2023Review(s) Completed, Editorial Evaluation Pending
25 Jun 2023Reviewer(s) Assigned
09 Aug 2023Editorial Decision: Revise Minor