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Distributed Design of Structured Optimal Controllers Using Chordal Decomposition

Belbasi, Mohammad Reza | 2021

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 54295 (05)
  4. University: Sharif University of Technology
  5. Department: Electrical Engineering
  6. Advisor(s): Babazadeh, Maryam
  7. Abstract:
  8. This thesis addresses the distributed optimal control problem. In order to solve this problem a suboptimal distributed design approach has been developed using tools from graph theory and optimization theory. The first objective of this thesis is overcoming the non-scalability of distributed control problems for larges -scale systems. The second objective is using minimum information of other subsystems in the design layer. First, the problems of designing a structured controller minimizing the H_2 and H_∞ norms of the closed-loop system have been formulized and stated as semidefinite optimization problems. Then in order to use the fundamental results that links the chordal graphs and semidefinite programming, the structured optimal control problems have been analyzed from graph theory perspective. Using these analyses, large-scale optimal control problems have been decomposed to several problems with lower dimensions.Second to solve the decomposed problems, using tools from distributed optimization, distributed design approaches have been developed and presented as separate algorithms for H_2 and H_∞ distributed control problems. Due to the lower dimension of the decomposed problems, the distributed design algorithms are more scalable and superior in keeping each subsystem’s information private. These algorithms also guarantee stability of the closed-loop systems.Finally, the efficiency and generalizability of the proposed algorithms are shown by testing them on several systems. The results of the simulation for large-scale systems indicates the remarkably lower implementation time and information sharing among subsystems for distributed algorithms compared to central design approaches. Also testing the algorithms for general networks with random structures shows the generalizability of the proposed methods
  9. Keywords:
  10. Semidefinite Programming ; Convex Optimization ; Distributed Optimal Control ; Chordal Graphs ; Distributed Design ; Graph Decomposition

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