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Analysis of Structured Controllers Stabilization: A Graph Theoretic Approach

Mosalli, Hesamoddin | 2019

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 52748 (05)
  4. University: Sharif University of Technology
  5. Department: Electrical Engineering
  6. Advisor(s): Babazadeh, Maryam
  7. Abstract:
  8. In this thesis, a new method is proposed to find the class of stabilizing control structures for interconnected systems from a graphtheoretic
    perspective. The objective is to classify all possible control structures (static or dynamic), capable of stabilizing the closedloop system. The method can be formulated by using the characteristics of fixed modes of the system for arbitrary control structures.To this end, first, a method is proposed based on solving a set of discrete linear programming to determine whether a system is stabilizable via a decentralized controller. Subsequently, by solving a set of discrete linear feasibility problems, all possible stabilizing controller structures are derived. In the first step, the decentralized fixed modes of the system are determined through assigning a bipartite graph to each mode of the system, and subsequently, a set of discrete linear optimization problems are developed. The proposed method seems remarkable from two main perspectives. First, to the best of our knowledge, there has not been any available systematic method, to check the stabilizability of a largescale system by means of a decentralized controller and the developed method is the first one of this kind. Moreover, since the proposed optimization problem tends to find all the maximal subgraphs of a bipartite graph, its application is not limited to the current case and finds utility in similar problems in the field of graph theory.In the second step, a discrete linear feasibility problem is formulated in a similar manner,and the set of its possible solutions provide all stabilizing control structures for each mode. It is notable that the existence of a static stabilizing controller which belongs to the resultant structures is ensured. Thus it would not be necessary to exploit a dynamic controller to stabilize the closedloop system.Finally, it is demonstrated that the utility of the proposed graphtheoretic approach is not limited to the analysis of stabilizing control structures, and it basically provides a framework to find the set of control structures capable of poleplacement of the closedloop
    system in any desired region
  9. Keywords:
  10. Graph Theory ; Bipartite Graph ; Structured Controller ; Stabilizing Controller Structures ; Fixed Mode

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