A Generalized Interval Observer Design for Nonlinear Discrete-Time Systems Using the Kazantzis-Kravaris/Luenberger (KKL) Approach

Conceitos Básicos

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.

Resumo

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.

Estatísticas

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Principais Insights Extraídos De

A Unified KKL-based Interval Observer for Nonlinear Discrete-time Systems

by Thach Ngoc D... às arxiv.org 04-30-2024

https://arxiv.org/pdf/2401.14505.pdf

Perguntas Mais Profundas

How can the proposed interval observer design be extended to handle time-varying nonlinear systems or systems with unknown disturbances

The proposed interval observer design can be extended to handle time-varying nonlinear systems or systems with unknown disturbances by incorporating adaptive mechanisms into the observer framework. For time-varying systems, the observer parameters can be adjusted dynamically based on the changing dynamics of the system. This adaptation can be achieved by introducing time-varying gains or updating the observer structure based on real-time system measurements. Additionally, for systems with unknown disturbances, the observer can be augmented with robust estimation techniques to account for the uncertainties in the system. By incorporating adaptive and robust features into the observer design, the framework can effectively handle the complexities introduced by time-varying dynamics and unknown disturbances in nonlinear systems.

What are the potential limitations or drawbacks of the KKL-based interval observer approach compared to other interval observer design methods for nonlinear systems

While the KKL-based interval observer approach offers a generic and systematic method for designing interval observers for nonlinear systems, there are potential limitations and drawbacks compared to other interval observer design methods. One limitation is the computational complexity involved in determining the transformation function T and its inverse T∗, especially for high-dimensional systems. The nonlinearity and complexity of the transformation can make it challenging to compute the observer bounds efficiently. Additionally, the conservativeness of the observer bounds may lead to wider intervals, reducing the accuracy of state estimation. Furthermore, the requirement for Lipschitz injectivity of the transformation may impose restrictions on the observability properties of the system, limiting the applicability of the KKL-based interval observer to certain classes of systems.

Can the proposed framework be adapted to address other estimation problems, such as fault detection or parameter estimation, for nonlinear discrete-time systems

The proposed framework can be adapted to address other estimation problems, such as fault detection or parameter estimation, for nonlinear discrete-time systems by modifying the observer design objectives and constraints. For fault detection, the interval observer can be enhanced with residual generation mechanisms to detect deviations between the estimated state and the actual system behavior. By analyzing the residuals using fault detection algorithms, the observer can identify and isolate potential faults in the system. Similarly, for parameter estimation, the observer structure can be modified to estimate unknown parameters in the system dynamics. By incorporating parameter identification techniques into the observer design, the framework can be utilized to estimate and track the variations in system parameters over time, enhancing the overall estimation capabilities for nonlinear discrete-time systems.