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Stabilizing control structures: An optimization framework

Mosalli, H ; Sharif University of Technology | 2021

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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 , 2021
  4. Abstract:
  5. This paper 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 (BLP). To carry out the primary goal, first, the stabilizability of an 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. IEEE
  6. Keywords:
  7. 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 ; 2021 ; 00189286 (ISSN)
  9. URL: https://ieeexplore.ieee.org/document/9521759