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A data-driven guaranteed zonotopic estimation for unknown time-varying system.

Xiang Ma1, Xinggao Liu1

  • 1School of Control Science and Engineering, Zhejiang University, Hangzhou 310058, China.

ISA Transactions
|October 17, 2024
PubMed
Summary
This summary is machine-generated.

This study presents a data-driven method for state estimation in unknown time-varying systems using zonotopic reachability analysis. The approach ensures system states remain within a compact, guaranteed estimation range.

Keywords:
Data-drivenState estimationTime-varying systemZonotope

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Area of Science:

  • Control Systems Engineering
  • Systems Theory
  • Applied Mathematics

Background:

  • Time-varying systems are prevalent but challenging due to unpredictable parameter changes.
  • Accurate modeling of these systems is often infeasible, necessitating data-driven approaches.
  • Existing state estimation methods struggle with unknown dynamics and time-varying parameters.

Purpose of the Study:

  • To develop a data-driven state estimation technique for discrete time-varying systems with unknown models.
  • To provide guaranteed bounds for system state estimation using reachability analysis.
  • To ensure the compactness and validity of the state estimation results.

Main Methods:

  • Utilizing zonotopic reachability analysis to handle uncertainty in system models.
  • Computing a time-varying matrix zonotope encompassing all possible system models from prior data.
  • Iteratively obtaining an over-approximated reachable zonotope for system states.
  • Proving the boundedness of the reachable zonotope using a P-radius definition.

Main Results:

  • A method to compute an over-approximated reachable zonotope for unknown discrete time-varying systems.
  • Guaranteed inclusion of the actual system state within the computed estimation range.
  • Demonstrated compactness of the state estimation results.
  • Validation through a numerical example and a circuit system simulation.

Conclusions:

  • The proposed data-driven method effectively estimates states for unknown time-varying systems.
  • Zonotopic reachability analysis provides a robust framework for handling model uncertainty.
  • The method ensures reliable and compact state estimation, applicable to real-world systems.