| 摘要: | 本博士論文針對一類渾沌系統提出一套估測不變集 (Invariant Set) 與解集合 (Solution Bound) 的方法，並提出三種控制方法論，確保主僕系統同步化能夠被實現，此外以模糊控制法則、非線性控制法則與線性控制法則，分別實現於廣義渾沌系統 (Generalized Chaotic System)、聯合渾沌系統 (Unified Chaotic System) 與廣義羅倫茲渾沌系統 (Generalized Lorenz Chaotic System)。首先藉由已導出的不變集與解集合之輔助，使得指數同步化控制器能以簡單的線性控制被實現。接著，基於Lyapunov定理、強健控制及有限時間穩定度概念，所提出的三種有限時間同步化控制方法已被實現。在模糊控制設計方面，Takagi–Sugeno 模糊模型被用來精確描述廣義主僕渾沌系統，且具有雜訊衰減能力的 H∞ 有限時間同步化控制器也已被合成，成功實現有限時間主僕同步化。在非線性控制設計上，具有強健性的非線性控制器已被設計，以確保系統在具有未知項的形況下，依然能夠成功實現有限時間主僕同步化。在線性控制器的設計上，藉由解集合的輔助，已成功設計出簡單的線性控制器，較值得一提的是該系統能夠事先指定收斂時間，並保證於規定時間內完成有限時間主僕同步化。所有設計的有限時間同步控制器，皆具有兩項可調參數，即指數收斂率與有限時間收斂率。此外基於模糊模型的有限時間同步控制器已被成功應用於保密通訊，並藉由FPGA與電腦設備，將保密系統實現於實際硬體電路上。最後輔以數值範例加以說明，其模擬結果已證明所提出之有限時間同步控制方法具備有效性與正確性，且成功地以實際實驗將保密通訊系統實現於硬體電路上。This dissertation presents an approach to estimate the invariant set and solution bound for a class of chaotic system, and proposes three methods, including fuzzy control, nonlinear and linear control to achieve master-slave synchronization (MSS) for generalized chaotic system, unified chaotic system and generalized Lorenz chaotic system, respectively. First of all, since the invariant set and solution bound are derived, the exponential synchronization can be achieved using a simple linear control law which is very easy implemented. Subsequently, based on Lyapunov theory, robust control, and the concept of the finite–time stability, three methods are proposed to achieve the finite-time synchronization (FTS). In fuzzy control design, Takagi–Sugeno (T–S) fuzzy models are utilized to exactly represent the master and slave chaotic systems, and the H∞ FTS controller is synthesized to achieve FTS with the minimum disturbance attenuation level. In nonlinear control design, the nonlinear controller is synthesized to achieve robust FTS for a class of uncertain unified chaotic system. In the linear control design, based on the auxiliary of solution bound, a simple linear control law is proposed to achieve FTS within a pre–specified convergence time. In addition, all of the proposed FTS controllers are with two adjustable parameters, namely, exponential convergence rate and finite–time convergence rate. Finally, the fuzzy–model–based FTS is applied to secure communication, and its hardware implementation with a field– programmable gate array (FPGA) chip and a personal computer is realized too. Moreover, simulated examples are given to show the feasibility and correctness of the proposed control criteria, and the proposed methods are successfully verified by the practical experiments. |
