本論文提出了一個基於Wiener模式所發展出一種新型遞迴類神經網路，其結合了相關具系統化的鑑別演算法來對動態系統鑑別並找出其最小狀態空間表示式。此一新穎的類神經網路包含了下列幾項優點: 1) 線性動態子系統及非線性靜態子系統可以將系統輸出表示成一個經由非線性轉換之線性狀態空間表示的網路； 2) 網路的特性可經由發展成熟且完整的線性系統理論來分析其狀態空間表示而得知；3) 此網路架構的大小可以由未知動態系統的狀態變數數目來決定。為了有效的利用未知動態系統的輸入輸出資料來加以鑑別，我們發展了一套包含維度估測、參數初始化及參數學習方法的系統化鑑別演算法。False nearest neighbors (FNN)演算法將利用輸入輸出資料所找出的最小嵌入維度當作系統的維度；eigensystem realization algorithm (ERA)利用所判定出來的維度來加以初始化狀態空間表示的參數。最後，為了更進一步的改善整個鑑別的效能，我們利用以ordered derivatives為基礎的遞迴參數學習方法來使最小狀態空間表示的參數達到最佳化。將未知動態系統以Wiener型遞迴類神經網路鑑別後，我們可以設計一個簡易但有效之線性迴饋控制器來執行對未知動態系統的控制任務。經由電腦模擬可得知，利用本論文所提出的演算法來進行動態系統鑑別已經成功地驗證了下列兩點: 1) 此遞迴類神經網路的維度是最小的； 2) 此網路能非常精確地模擬未知系統的動態行為並達到滿意的效能； 3) 此控制方法可以成功地被驗證其對於未知非線性系統控制問題之效能。

This study presents a Wiener-type recurrent neural network with a systematic identification algorithm and a control strategy for identifying and controlling unknown dynamic nonlinear systems. The proposed Wiener-type recurrent network resembles the conventional Wiener model that consists of a dynamic linear subsystem cascaded with a static nonlinear subsystem. The novelties of our network include: 1) the two subsystems are integrated into a single network whose output is expressed by a nonlinear transformation of a linear state-space equation; 2) the characteristics of the trained network can be analyzed by its associated state-space equation using the well-develop theory of linear systems; and 3) the size of the network structure is determined by the number of state variables (or the system order) of the unknown systems to be identified. A systematic identification algorithm that consists of an order determination procedure, a parameterization procedure, and an online learning procedure has been developed to effectively identify unknown systems from their input-output data. The false nearest neighbors (FNN) algorithm was adopted to acquire a minimal embedding dimension from the input-output data as the system order, and then the eigensystem realization algorithm (ERA) was used to initialize a best-fit state-space representation according to the acquired system order. To improve the overall identification performance, an online parameter learning algorithm based on an ordered derivatives and momentum terms has been derived. Subsequently, a simple feedback linear controller can be designed to control the unknown dynamic nonlinear systems without much complexity. Computer simulations on dynamic system identification and control problems have successfully validated the followings: 1) the dimension/order of the recurrent network representation is minimal, 2) the proposed network is able to closely emulate the behavior of the unknown dynamical system with a satisfactory performance, and 3) the proposed control scheme can control unknown nonlinear systems successfully.

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