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Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
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The frequency-domain technique, commonly used in analyzing and designing feedback control systems, is effective for linear, time-invariant systems. However, it falls short when dealing with nonlinear, time-varying, and multiple-input multiple-output systems. The time-domain or state-space approach addresses these limitations by utilizing state variables to construct simultaneous, first-order differential equations, known as state equations, for an nth-order system.
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Nonlinear state estimation by Extended Parallelotope Set-Membership Filter.

Danyang Qu1, Zheng Huang1, Yiwen Zhao1

  • 1State Key Laboratory of Robotics, Shenyang Institute of Automation, Chinese Academy of Sciences, Shenyang 110016, China; Institutes for Robotics and Intelligent Manufacturing, Chinese Academy of Sciences, Shenyang 110016, China; University of Chinese Academy of Sciences, Beijing 100049, China.

ISA Transactions
|December 22, 2021
PubMed
Summary

We introduce the Extended Parallelotope Set-Membership Filter for improved state estimation in nonlinear systems. This method reduces redundancy, enhancing accuracy over existing techniques.

Keywords:
FilterNonlinearParallelotopesSet membershipState estimation

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Area of Science:

  • Control Systems Engineering
  • Nonlinear Dynamics
  • Estimation Theory

Background:

  • Existing state estimation methods for discrete-time nonlinear systems suffer from redundancy during iteration, degrading accuracy.
  • Noise envelope processing in conventional filters often introduces significant errors.
  • Accurate state estimation is crucial for the performance of many dynamic systems.

Purpose of the Study:

  • To propose a novel state estimation method, the Extended Parallelotope Set-Membership Filter (EPSMF), for discrete-time nonlinear systems.
  • To address and mitigate the redundancy issue inherent in existing iterative estimation algorithms.
  • To enhance the accuracy of state estimation compared to current state-of-the-art methods.

Main Methods:

  • Developed an innovative parallelotope envelope method to reduce redundancy from noise envelope processing.
  • Designed a cofactor separation method for nonlinear systems to achieve a tight parallelotope set envelope.
  • Created a novel parallelotope intersection method for updating the state set within the parallelotope envelope framework.

Main Results:

  • The Extended Parallelotope Set-Membership Filter demonstrates superior state estimation accuracy.
  • Simulation results confirm the effectiveness and reduced redundancy of the proposed EPSMF.
  • The method outperforms conventional techniques in both maximum and average state estimation accuracy.

Conclusions:

  • The Extended Parallelotope Set-Membership Filter offers a significant advancement in state estimation for discrete-time nonlinear systems.
  • The proposed parallelotope envelope and intersection methods effectively reduce redundancy and improve accuracy.
  • EPSMF provides a more reliable and accurate approach to state estimation in complex nonlinear dynamic environments.