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Stabilizing control structures: An optimization framework

Mosalli, H ; Sharif University of Technology | 2022

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  1. Type of Document: Article
  2. DOI: 10.1109/TAC.2021.3107247
  3. Publisher: Institute of Electrical and Electronics Engineers Inc , 2022
  4. Abstract:
  5. This article presents a new optimization-based approach to determine the class of stabilizing control structures with the necessary set of feedback links for interconnected systems. The proposed approach relies on a graph-theoretic interpretation and its equivalence in terms of binary linear programs (BLPs). To carry out the primary goal, first, the stabilizability of a linear time-invariant (LTI) system under the decentralized control structure is presented in terms of a BLP. Next, two graph-based criteria are proposed to characterize stabilizing control structures with the required feedback links. Finally, all possible stabilizing control structures with the necessary feedback links are derived via solving a set of BLPs. In addition to the analysis of stabilizing control structures, the proposed graph-theoretic approach offers a versatile set of tools to find the simplest control structures capable of assigning the closed-loop spectrum in a totally arbitrary desired region. Simulation results illustrate the assessment of stabilizing control structures, the required additional feedback links, and the elegant generalization of the proposed approach to regional pole-placement. © 1963-2012 IEEE
  6. Keywords:
  7. Bipartite graph ; Fixed-mode ; Stabilizing controllers ; Feedback ; Graph theory ; Graphic methods ; Linear control systems ; Linear programming ; Linear systems ; Structural optimization ; Binary linear program ; Control structure ; Graph theoretic approach ; Graph-theoretic ; Optimization framework ; Regional pole placement ; Stabilizability ; Stabilizing control ; Decentralized control
  8. Source: IEEE Transactions on Automatic Control ; Volume 67, Issue 7 , 2022 , Pages 3738-3745 ; 00189286 (ISSN)
  9. URL: https://ieeexplore.ieee.org/document/9521759?denied