Adaptive Observer for a Class of Systems with Switched Unknown Parameters Using DREM

Tong Liu, Zengjie Zhang, Fangzhou Liu (Corresponding author), Martin Buss

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Abstract

In this note, we develop an adaptive observer for a class of nonlinear systems with switched unknown parameters to estimate the states and parameters simultaneously. The main challenge lies in how to eliminate the disturbance effect of zero-input responses caused by the switching on the parameter estimation. These responses depend on the unknown states at switching instants (SASI) and constitute an additive disturbance to the parameter estimation, which obstructs parameter convergence to zero. Our solution is to treat the zero-input responses as excitations instead of disturbances. This is realized by first augmenting the system parameter with the SASI and then developing an estimator for the augmented parameter using the dynamic regression extension and mixing technique. Thanks to its property of elementwise parameter adaptation, the system parameter estimation is decoupled from the SASI. As a result, the estimation errors of system states and parameters converge to zero asymptotically. Furthermore, the robustness of the proposed adaptive observer is guaranteed in the presence of disturbances and noise. A numerical example validates the effectiveness of the proposed approach.

Original languageEnglish
Article number10232851
Pages (from-to)2445-2452
Number of pages8
JournalIEEE Transactions on Automatic Control
Volume69
Issue number4
Early online date28 Aug 2023
DOIs
Publication statusPublished - Apr 2024

Funding

This work was supported in part by the National Natural Science Foundation of China under Grant 62373123 and Grant 62173147.

Keywords

  • Adaptive observer
  • Adaptive systems
  • Convergence
  • Estimation error
  • Observers
  • Parameter estimation
  • State observer
  • Switched systems
  • Switches
  • switched systems
  • state observer
  • parameter estimation

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