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Pré-Publication, Document De Travail Année : 2024

Interval KKL Observer for Uncertain Discrete Time-Varying Nonlinear Systems

Résumé

Kazantzis-Kravaris/Luenberger (KKL) or Nonlinear Luenberger observers are powerful theoretical tools used to estimate the state of a very large class of nonlinear systems. Such observers rely on the existence of an injective transformation towards new coordinates in which the original system dynamics becomes an exponentially stable linear filter of the output, and thus easy to estimate. The injectivity of the transformation enables to use its left inverse in order to recover the original system state estimate in the original coordinates. The existence of such an injective transformation may be guaranteed under a backwarddistinguishability assumption of the original system. The present paper proposes an interval observer, i.e. a lower and an upper bound of the actual state, based on the KKL principle, for a discrete-time time-varying nonlinear system subject to additive bounded disturbances and measurement noise. The design of this observer mainly relies on the existence of uniform Lipschitz backward distinguishability assumption enabling to bound the state regarding the uncertainties using an interval observer for the linear filter in the new coordinates. In the original coordinates, the inclusion of the system state into the estimated interval and the boundedness of the errors are guaranteed after a finite time. Some practical considerations regarding implementation of a such observer are addressed and a numerical example illustrates the resulting performances.
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Dates et versions

hal-04529711 , version 1 (02-04-2024)
hal-04529711 , version 2 (02-05-2024)

Identifiants

  • HAL Id : hal-04529711 , version 2

Citer

Antoine Hugo, Luc Meyer, Hélène Piet-Lahanier, Rihab El Houda Thabet, Sofiane Ahmed Ali. Interval KKL Observer for Uncertain Discrete Time-Varying Nonlinear Systems. 2024. ⟨hal-04529711v2⟩
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