Core Concepts
This work proposes a unified interval observer design framework for nonlinear discrete-time systems based on the Kazantzis-Kravaris/Luenberger (KKL) paradigm, without any assumptions on the structure of the system's dynamics and output maps.
Abstract
The authors present an interval observer design for nonlinear discrete-time systems using the Kazantzis-Kravaris/Luenberger (KKL) approach. The key highlights are:
The proposed design extends to generic nonlinear systems without any assumption on the structure of the system's dynamics and output maps. This is in contrast to existing works that focus on nonlinear systems with specific structural assumptions.
The design relies on transforming the original system into a target form where an interval observer can be directly designed. The authors then propose a method to reconstruct the bounds in the original coordinates using the bounds in the target coordinates, thanks to the Lipschitz injectivity of the transformation.
The effectiveness of the proposed interval observer is demonstrated through an academic example, showing its ability to provide guaranteed state estimation bounds even in the presence of uncertainties.
The authors highlight that the proposed framework serves as a first milestone towards a more general and systematic method for designing interval observers for nonlinear systems, addressing the challenge of lacking generality in existing approaches.
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