A new approach to constrained state estimation for discrete-time linear systems with unknown inputs

J.F. Garcia Tirado, A. Marquez-Ruiz, H. Botero Castro, F. Angulo

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Abstract

This paper addresses the problem of estimating the state for a class of uncertain discrete-time linear systems with constraints by using an optimization-based approach. The proposed scheme uses the moving horizon estimation philosophy together with the game theoretical approach to the H∞ filtering to obtain a robust filter with constraint handling. The used approach is constructive since the proposed moving horizon estimator (MHE) results from an approximation of a type of full information estimator for uncertain discrete-time linear systems, named in short H∞-MHE and H∞-full information estimator, respectively. Sufficient conditions for the stability of the H∞-MHE are discussed for a class of uncertain discrete-time linear systems with constraints. Finally, since the H∞-MHE needs the solution of a complex minimax optimization problem at each sampling time, we propose an approximation to relax the optimization problem and hence to obtain a feasible numerical solution of the proposed filter. Simulation results show the effectiveness of the robust filter proposed.

Original languageEnglish
Pages (from-to)326–341
JournalInternational Journal of Robust and Nonlinear Control
Volume28
Issue number1
DOIs
Publication statusPublished - 1 Jan 2018

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State estimation
Linear systems
Sampling

Keywords

  • Constrained estimation
  • Moving horizon estimation
  • Optimization
  • Robust estimation
  • Uncertain linear systems

Cite this

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title = "A new approach to constrained state estimation for discrete-time linear systems with unknown inputs",
abstract = "This paper addresses the problem of estimating the state for a class of uncertain discrete-time linear systems with constraints by using an optimization-based approach. The proposed scheme uses the moving horizon estimation philosophy together with the game theoretical approach to the H∞ filtering to obtain a robust filter with constraint handling. The used approach is constructive since the proposed moving horizon estimator (MHE) results from an approximation of a type of full information estimator for uncertain discrete-time linear systems, named in short H∞-MHE and H∞-full information estimator, respectively. Sufficient conditions for the stability of the H∞-MHE are discussed for a class of uncertain discrete-time linear systems with constraints. Finally, since the H∞-MHE needs the solution of a complex minimax optimization problem at each sampling time, we propose an approximation to relax the optimization problem and hence to obtain a feasible numerical solution of the proposed filter. Simulation results show the effectiveness of the robust filter proposed.",
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A new approach to constrained state estimation for discrete-time linear systems with unknown inputs. / Garcia Tirado, J.F.; Marquez-Ruiz, A.; Botero Castro, H.; Angulo, F.

In: International Journal of Robust and Nonlinear Control, Vol. 28, No. 1, 01.01.2018, p. 326–341.

Research output: Contribution to journalArticleAcademicpeer-review

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AB - This paper addresses the problem of estimating the state for a class of uncertain discrete-time linear systems with constraints by using an optimization-based approach. The proposed scheme uses the moving horizon estimation philosophy together with the game theoretical approach to the H∞ filtering to obtain a robust filter with constraint handling. The used approach is constructive since the proposed moving horizon estimator (MHE) results from an approximation of a type of full information estimator for uncertain discrete-time linear systems, named in short H∞-MHE and H∞-full information estimator, respectively. Sufficient conditions for the stability of the H∞-MHE are discussed for a class of uncertain discrete-time linear systems with constraints. Finally, since the H∞-MHE needs the solution of a complex minimax optimization problem at each sampling time, we propose an approximation to relax the optimization problem and hence to obtain a feasible numerical solution of the proposed filter. Simulation results show the effectiveness of the robust filter proposed.

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