Optimal design of reduced-order observers with specified eigenvalues and performance measurement of minimizing estimation errors using evolutionary optimization

Fu I. Chou, Ming-Yang Cheng

Research output: Contribution to journalArticle

Abstract

A new method is proposed in this paper which designs a reduced-order observer of a non-observable-form-based dynamical system such that: (i) the eigenvalues are specified to satisfy desired convergence performance, (ii) a full-rank condition is satisfied, and (iii) a quadratic performance measurement of the deviation of the estimates from the actual states is minimized so as to reduce the large error occurring during the transient period of observation. The proposed approach combines the merits of both the orthogonal functions approach and evolutionary optimization. By solving a Sylvester equation, the proposed optimal design method can not only be used to design the reduced-order observer of a non-observable-form-based dynamical system, but also can avoid the shortcomings of approaches already existing in relevant literatures. Two examples are given to demonstrate the effectiveness and efficiency of the proposed new optimization method on the performance of state estimations. From the demonstrative examples, it can be seen that the estimated state errors asymptotically converge quickly to zero. In addition, the performance measurement values based on the proposed optimal design approach are apparently much lower than those based on the existing nonoptimal design method.

Original languageEnglish
Pages (from-to)728-739
Number of pages12
JournalJournal of Low Frequency Noise Vibration and Active Control
Volume38
Issue number2
DOIs
Publication statusPublished - 2019 Jun 1

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eigenvalue
Error analysis
eigenvalues
design method
optimization
Dynamical systems
Orthogonal functions
dynamical systems
State estimation
state estimation
orthogonal functions
Optimal design
deviation
estimates
method

All Science Journal Classification (ASJC) codes

  • Civil and Structural Engineering
  • Building and Construction
  • Acoustics and Ultrasonics
  • Mechanics of Materials
  • Geophysics
  • Mechanical Engineering

Cite this

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abstract = "A new method is proposed in this paper which designs a reduced-order observer of a non-observable-form-based dynamical system such that: (i) the eigenvalues are specified to satisfy desired convergence performance, (ii) a full-rank condition is satisfied, and (iii) a quadratic performance measurement of the deviation of the estimates from the actual states is minimized so as to reduce the large error occurring during the transient period of observation. The proposed approach combines the merits of both the orthogonal functions approach and evolutionary optimization. By solving a Sylvester equation, the proposed optimal design method can not only be used to design the reduced-order observer of a non-observable-form-based dynamical system, but also can avoid the shortcomings of approaches already existing in relevant literatures. Two examples are given to demonstrate the effectiveness and efficiency of the proposed new optimization method on the performance of state estimations. From the demonstrative examples, it can be seen that the estimated state errors asymptotically converge quickly to zero. In addition, the performance measurement values based on the proposed optimal design approach are apparently much lower than those based on the existing nonoptimal design method.",
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N2 - A new method is proposed in this paper which designs a reduced-order observer of a non-observable-form-based dynamical system such that: (i) the eigenvalues are specified to satisfy desired convergence performance, (ii) a full-rank condition is satisfied, and (iii) a quadratic performance measurement of the deviation of the estimates from the actual states is minimized so as to reduce the large error occurring during the transient period of observation. The proposed approach combines the merits of both the orthogonal functions approach and evolutionary optimization. By solving a Sylvester equation, the proposed optimal design method can not only be used to design the reduced-order observer of a non-observable-form-based dynamical system, but also can avoid the shortcomings of approaches already existing in relevant literatures. Two examples are given to demonstrate the effectiveness and efficiency of the proposed new optimization method on the performance of state estimations. From the demonstrative examples, it can be seen that the estimated state errors asymptotically converge quickly to zero. In addition, the performance measurement values based on the proposed optimal design approach are apparently much lower than those based on the existing nonoptimal design method.

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