本文利用minimax H_∞ 隨機博弈策略，提出了一種新穎的強健分散式模型追蹤控制設計架構，用於線性和非線性在具有外部干擾和其他子系統間的時變延遲耦合情況下的大規模隨機互聯系統。所提出用於強健分散式模型追蹤控制的隨機minimax H_∞博弈策略中，從保守的觀點來看，外部干擾以及與子系統間的耦合被比擬為會惡化子系統追蹤性能的一個玩家，而當子系統的控制器被認為是另一個玩家時，從隨機H_∞博弈論的觀點可以最小化它們對追蹤性能最糟情況的影響。通過所提出的minimax H_∞隨機博弈策略，可以有效地衰減外部干擾和來自其他子系統的時變延遲耦合對模型追蹤的最壞情況影響。並且，可以實現對於每個子系統的強健分散式H_∞模型追蹤。在線性隨機互聯系統中，基於minimax H_∞ 博弈策略的角度，強健分散式追蹤控制設計轉變為求解在線性矩陣不等式（LMIs）的最佳化問題。在非線性隨機互聯系統中，設計minimax H_∞分散式追蹤控制時，我們需要先解決Hamilton-Jacobi Isaacs不等式（HJIIs）的最佳化問題。基於全局線性化（Global Linearization）技術，HJIIs的最佳化問題可以轉化為LMIs最佳化問題，用於非線性隨機互聯系統的強健分散式追蹤控制。最後，給出了three-machine power system貨物搬運過程的模擬例子，說明了所提出的強健分散式追蹤架構的有效性。

In this study, using a minimax H_∞ stochastic game strategy, a novel robust decentralized model reference tracking control design is proposed for linear and nonlinear stochastic interconnected large-scale systems with external disturbance and time-varying delay couplings from other subsystems. In the proposed stochastic minimax H_∞ game strategy for robust decentralized model reference tracking control, to be on the safe side, external disturbance and time-varying delay couplings from other subsystems are considered as one player to deteriorate the tracking performance of each subsystem as fully as possible when the controller of the subsystem is considered as the other player to minimize their worst-case effects on the tracking performance from the stochastic H_∞ game perspective. By the proposed minimax H_∞ stochastic game strategy, the worst-case effect of external disturbance and time-varying delay couplings from other subsystems on the model reference tracking could be efficiently attenuated. Then, the robust decentralized H_∞ model reference tracking for each subsystem could be achieved. In the linear stochastic interconnected system, the robust decentralized tracking control design based on the minimax H_∞ game strategy becomes a linear matrix inequalities (LMIs)-constrained optimization problem. In the nonlinear stochastic interconnected system, we need to solve a Hamilton-Jacobi Isaacs inequalities (HJIIs)-constrained optimization problem for the minimax H_∞ decentralized tracking control design. Based on the global linearization technique, the HJIIs-constrained optimization problem could be transformed to an LMIs-constrained optimization problem for the robust decentralized tracking control of nonlinear stochastic interconnected system. Finally, a simulation example of three-machine power system is given to illustrate the effectiveness of the proposed robust decentralized tracking scheme in the shipping process of goods delivery.

摘要 ---------------------------------- i
Abstract ------------------------------ ii
Content ------------------------------- iii
I.Introduction ------------------------ 1
II.Problem Formulation and Robust Decentralized Model Reference Tracking Control Design for Linear Stochastic Interconnected Systems ------------------------------- 3
III.Robust Decentralized Model Reference Tracking Control Design for Nonlinear Stochastic Interconnected Network Systems ------------------------------------------------- 8
IV.Simulation Example ----------------- 13
V.Conclusion -------------------------- 17
Appendix A ---------------------------- 18
Appendix B ---------------------------- 20
Appendix C ---------------------------- 21
Appendix D ---------------------------- 23
Appendix E ---------------------------- 25
References ---------------------------- 27

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