具自動建構特性之模糊與類神經網路控制架構於非線性動態系統之應用

Abstract

為解決非線性系統控制問題，本論文發展兩個嶄新的控制架構。首先針對非仿射的非線性動態系統，提出具自我建構特性的強健適應性模糊控制架構。此架構中的控制器包含一個自我建構的模糊控制器和一個強建控制器。自我建構的模糊控制器用來近似未知的系統非線性，並可以自動刪除及產生模糊規則以建立簡潔的模糊規則庫;強健控制器用來達成L2追蹤表現，並抑制誤差至要求的範圍以使系統穩定。我們舉出四個例子顯示此控制架構不但能有良好的控制表現，也可大量減少運算量。其次針對仿射的非線性動態系統，提出使用以霍普菲爾為基礎的動態類神經網路的直接適應性控制架構。在此架構中，以霍普菲爾為基礎的動態類神經網路用來近似一個理想控制器；監督控制器則用來抑制近似誤差和外界干擾的影響。藉由Lypunov方法可堆導出適應法則，用以調整網路的權重值使得系統穩定。經由適當地選取參數，可將追蹤物差抑制到要求的範圍內。經由模擬證實了此架構的可行性及良好效果。僅含一個神經元的以霍普菲爾為基礎的動態類神經網路使得此架構易於以硬體實現，另外，我們亦探討由無自我回授神經元建構而成的以霍普菲爾為基礎的動態類神經網路。經比較發現，採用具有自我回授神經元的以霍普菲爾為基礎的動態類神經網路之控制架構，其控制表現較佳。值得注意的是，本論文中所提出的自我建構模糊系統和固定架構的以霍普菲爾為基礎的動態類神經網路皆不需要專家的知識或是試誤過程來決定其架構，因此解決了模糊系統和類神經網路的架構問題。

In this dissertation, two novel control schemes are proposed to solve the control problems of nonlinear systems. The first is a robust adaptive self-structuring fuzzy control (RASFC) scheme for nonaffine nonlinear systems, and the second is a direct adaptive control scheme using Hopfield-based dynamic neural network (DACHDNN) for affine nonlinear systems. The RASFC scheme is composed of a robust adaptive controller and a self-structuring fuzzy controller. The design of the self-structuring fuzzy controller design utilizes a novel self-structuring fuzzy system (SFS) to approximate the unknown plant nonlinearity, and the SFS can automatically grow and prune fuzzy rules to realize a compact fuzzy rule base. The robust adaptive controller is designed to achieve a L2 tracking performance with a desired attenuation level to stabilize the closed-loop system. Four examples are presented to show that the proposed RASFC scheme can achieve favorable tracking performance and relieve heavy computational burden. In the DACHDNN, a Hopfield-based dynamic neural network is used to approximate the ideal controller, and a compensation controller is used to suppress the effect of approximation error and disturbance. The weightings of the Hopfield-based dynamic neural network are on-line tuned by the adaptive laws derived in the Lyapunov sense, so that the stability of the closed-loop system can be guaranteed. The tracking error can be attenuated to a desired level by adequately selecting some parameters. The case of Hopfield-based neural network without the self-feedback loop is also studied and shown to have inferior results than those of Hopfield neural network with the self-feedback loop. Simulation results illustrate the applicability of the proposed control scheme. The Hopfield-based dynamic neural network with a parsimonious structure has the best potential be realized in hardware. It should be emphasized that the self-structuring property of the SFS and the fixed parsimonious structure of the DACHDNN eliminate the need for expert’s knowledge or error-trial process and thus provide perfect solutions to the structuring problems of fuzzy systems and neural networks, respectively.