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Optimal static output feedback simultaneous regional pole placement.

Jenq-Lang Wu1, Tsu-Tian Lee

  • 1Electronic Engineering Department, Hwa Hsia Institute of Technology, Taipei, Taiwan. wujl@cc.hwh.edu.tw

IEEE Transactions on Systems, Man, and Cybernetics. Part B, Cybernetics : a Publication of the IEEE Systems, Man, and Cybernetics Society
|October 26, 2005
PubMed
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This study addresses optimal simultaneous regional pole placement for multiple linear systems using a single controller. A novel barrier method approach provides an approximate solution to this nonconvex optimization problem.

Area of Science:

  • Control Systems Engineering
  • Optimization Theory
  • Applied Mathematics

Background:

  • Simultaneous regional pole placement is crucial for designing controllers that ensure stability and performance for multiple systems.
  • Existing methods like linear matrix inequality (LMI) are insufficient for this nonconvex problem.

Purpose of the Study:

  • To develop a method for optimal simultaneous regional pole placement for a collection of linear time-invariant systems.
  • To address the limitations of current approaches for nonconvex optimization problems in control design.

Main Methods:

  • The study employs a barrier method to solve an auxiliary minimization problem, yielding an approximate solution.
  • Algorithms are developed for finding the optimal solution to the constrained optimization problem.

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Main Results:

  • A necessary and sufficient condition for the existence of admissible solutions is derived.
  • The barrier method provides an effective approximate solution for the nonconvex simultaneous regional pole placement problem.

Conclusions:

  • The proposed barrier method offers a viable approach to solving the complex problem of simultaneous regional pole placement.
  • The derived conditions and algorithms facilitate the design of single static output feedback controllers for multiple systems.