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Robust Scalable Control of Interconnected Systems using Chordal Graph Decomposition

Jafarzadeh, Samad | 2024

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 57845 (05)
  4. University: Sharif University of Technology
  5. Department: Electrical Engineering
  6. Advisor(s): Babazadeh, Maryam
  7. Abstract:
  8. In this thesis, the robust control problem of interconnected systems that are connected to each other with an arbitrary structure is investigated. A new approach based on distributed optimization design is used for solving this problem. This method exploits graph and optimization algorithms. The stability of controlled systems, overcoming convergence issue in high-dimensional problems, and minimum use of the other subsystem information are the primary objectives of this research. In the first step, polytopic uncertainties in the design of the minimum norm controller are formulated using the block diagonal Lyapunov matrix and expressed with semi-definite programs. The goal of this work is to exploit fundamental results that form a bridge between chordal graphs and semi-definite optimization problems. The optimal robust control problem has been analyzed and reviewed from the graph perspective. Then, with the help of obtained results and diagonal graph analysis, the high-dimensional problems have been decomposed into several low-dimensional problems. In the second step, using distributed optimization tools, a stable and distributed approach for solving the decomposed problems has been developed and expressed in the algorithmic form of robust distributed control of . The advantages of the developed algorithm compared to existing centralized approaches are high convergence speed, maintaining confidentiality of information, flexibility in managing and setting parameters, reduced communication costs, increasing efficiency and performance in updating model parameters. Finally, the performance, accuracy, and generalizability of the developed algorithms are evaluated on several systems with different characteristics. The simulation results for large scale systems show that the presented approach succeeds in robust control of distributed problems with high accuracy in a reasonable time and with a limited level of access to system information. The analyses conducted on various systems have shown that the developed algorithm has a high level of generalization capability and can be applied in a wide range of industrial and research applications. For example, robotic control, industrial manufacturing systems, autonomous vehicle control, smart power grids, aerospace, and defense industries are just a few potential applications of this algorithm
  9. Keywords:
  10. Robust Control ; Structural Control ; Chordal Graphs ; Distributed Design ; Convex Optimization ; Polytopic Uncertainty ; Alternating Direction Method of Multipliers (ADMM)Algorithm ; Edge-Based Alternating Direction Method of Multipliers (ADMM)Algorithm

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