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A Novel Approach to Mixed Model and Goal Coordination of Large-Scale Systems

Ramezani , Mohammad Hossein | 2009

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 39835 (05)
  4. University: Sharif University of Technology
  5. Department: Electrical Engineering
  6. Advisor(s): Sadati, Naser
  7. Abstract:
  8. In this thesis, a new approach is proposed for two-level optimal control of large-scale nonlinear systems. In this approach, by defining some parameters as coordination parameters the overall system is decomposed into several interactive subsystems, where the optimization problem redefines for each one of them. The obtained sub-problems which are in the form of standard optimal control problems with lower dimension are solved in the first level. To obtain the overall optimal solution, coordination of the first level solutions is performed in the second level. For solving the first level problems, the indirect gradient and Newton methods are used. The gradient method is applied in the first few iterations in which the solution is far from the optimal solution, but Newton method is preferred near the optimal point. In order to simplify the solution of nonlinear optimal control problems using the Newton method, a new closed form formulation is presented for derivation of the total Hessian matrix. Having this matrix, the application of Newton algorithm will be simplified to a high degree, in compare to the conventional Newton algorithm in which a two point boundary value problem should be solved in each iteration. It is also shown that in cases where the horizon of the cost function is finite, the presented formulation can improve the solution time of the problem, besides simplification. Regarding to the coordination problem, a new mixed method algorithm is proposed based on the interaction prediction principle. One of the advantages of this approach is its independency to the parameter's variation and also the initial guess of the coordination vector. In addition, the number of iterations is considerably reduced since the updating of the coordination vector directly causes the reduction of the coordination error in the proposed coordination strategy. The performance of the proposed approach in solving various problems, such as chemical and photochemical reactors, power system and distillation column, are shown through computer simulations. The results are also compared to the centralized method and the other two-level coordination approaches. In this thesis, a new approach is proposed for two-level optimal control of large-scale nonlinear systems. In this approach, by defining some parameters as coordination parameters the overall system is decomposed into several interactive subsystems, where the optimization problem redefines for each one of them. The obtained sub-problems which are in the form of standard optimal control problems with lower dimension are solved in the first level. To obtain the overall optimal solution, coordination of the first level solutions is performed in the second level. For solving the first level problems, the indirect gradient and Newton methods are used. The gradient method is applied in the first few iterations in which the solution is far from the optimal solution, but Newton method is preferred near the optimal point. In order to simplify the solution of nonlinear optimal control problems using the Newton method, a new closed form formulation is presented for derivation of the total Hessian matrix. Having this matrix, the application of Newton algorithm will be simplified to a high degree, in compare to the conventional Newton algorithm in which a two point boundary value problem should be solved in each iteration. It is also shown that in cases where the horizon of the cost function is finite, the presented formulation can improve the solution time of the problem, besides simplification. Regarding to the coordination problem, a new mixed method algorithm is proposed based on the interaction prediction principle. One of the advantages of this approach is its independency to the parameter's variation and also the initial guess of the coordination vector. In addition, the number of iterations is considerably reduced since the updating of the coordination vector directly causes the reduction of the coordination error in the proposed coordination strategy. The performance of the proposed approach in solving various problems, such as chemical and photochemical reactors, power system and distillation column, are shown through computer simulations. The results are also compared to the centralized method and the other two-level coordination approaches.


  9. Keywords:
  10. Large Scale System ; Optimal Control ; Interaction Prediction Principle ; Interaction Balance Principle ; Coordination Model ; Interaction Prediction Approach ; Two Level Control

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