Two-level Robust Control of Large-scale Systems

Rahmani, Mehdi | 2013

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 44098 (05)
  4. University: Sharif University of Technology
  5. Department: Electrical Engineering
  6. Advisor(s): Sadati, Naser
  7. Abstract:
  8. In this thesis, two-level optimal control of uncertain and non-uncertain large-scale systems is presented. In the proposed two-level approach, using a decomposition/coordination framework, the large-scale system is first decomposed into several interactive subsystems, at the first-level, where a smaller optimization problem is solved at each subsystem. At the second-level, a substitution type prediction method, as a coordination strategy, is used to predict the interaction between subsystems. The coordinator mainly evaluates the next update for the coordination parameters and continues to exchange information with the first-level, so that the overall optimum solution is obtained. It is shown that the capability of parallel processing, at the first-level, reduces the computation time in solving the overall optimization problem. For linear large-scale systems, using the solution of least square minimization problem, a new two-level approach is presented for optimal control of large-scale systems. Convergence rate, computation time and optimality of the proposed algorithm are compared with centralized, decentralized, and classic two-level approaches for linear large-scale systems. Also, extension of this algorithm for nonlinear largescale systems is presented and its performance and capabilities are investigated in comparison with the conventional gradient-type optimal controller. Moreover, for linear uncertain large-scale systems, using the least square minimization problems with bounded data uncertainty (BDU), a closed-form solution obtained as a feedback of states and interactions in each subsystem, and then by applying the same coordination strategy, the local solutions of subsystems are converged to the overall optimal solution for the whole large-scale system. This method is applicable to any large-scale system with unstructured and bounded uncertainties. Moreover, it does not have the limitation of most robust control approaches in having structured uncertainties or satisfying the so-called matching conditions. We remark that the model of interactions is directly used in this approach to solve the optimization problems. Therefore, it is not required to estimate interactions or consider their bounds in controller design, as often used in decentralized robust control techniques that result in suboptimal solutions. In addition, the proposed two-level robust optimal control approach is extended to apply in tracking problems, where the states are desired to track reference signals. Moreover, it is used to control uncertain large-scale systems with known time-delay in states and also it is applied for robust optimal control of nonlinear large-scale systems. In the area of robust control, it is a very challenging problem to optimize a performance index in presence of uncertainties for nonlinear and time-delayed systems. Finally, the effectiveness and performance of the proposed approach in solving various problems are discussed through several computer simulations
  9. Keywords:
  10. Optimization ; Decentralized Control ; Robust Control ; Large Scale System ; Coordination ; Hierarchical Structure

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