動態類神經網路在非線性系統鑑別與控制器設計之應用

Abstract

本計畫的主要目的在探討以霍普菲爾為基礎的類神經網路在非線性系統分析與設計的 線上學習作業和及時應用的理論與實際問題。以系統鑑別為例，其在許多控制方法的研 究中是相當重要的一環。正如我們所熟知，無論是靜態或動態類神經網路，應用於複雜 的非線性動態系統鑑別上都有相當好的效果。然而，近年來的研究成果顯示其中仍有若 干弱點。例如，靜態類神經網路須藉由分接延遲器才能正確地表現動態系統，因而限制 了其在系統鑑別上應用性；另一方面，多數的動態類神經網路應用於類神經網路時，無 法嚴格保證學習過程中誤差的收斂性。為解決這些缺點，本計劃將提出一個新的以霍普 菲爾為基礎的動態類神經網路，來完成非線性系統鑑別。我們將進行收斂性分析，並藉 由Lyapunov 方法來調整網路的權重值，藉此嚴格保証鑑別過程中的誤差收斂性。在第 一年的計畫中，我們將發展學習功能的演算法及強健程度的分析，並以電腦模擬驗證。 同時，我們也將探討自我回授於以霍普菲爾為基礎的動態類神經網路中的作用，藉以增 進非系統鑑別的準確度。於第二年計畫中，我們將以倒單擺系統和平衡球系統鑑別的硬 體實作來驗證本計劃的理論推導結果。在第三年計畫中，我們將針對仿射的非線性動態 系統，嘗試建立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。此一 架構不須要先進行系統鑑別，因而降低了系統複雜度並提高了硬體實現的可行性。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，藉由Lypunov 方法我們嘗試推導出適應法則，用來調整網路的權重值以保證系統穩定。此一控制器的 正確性將先以電腦模擬檢驗，最後以混沌電路的控制實作驗證其效果。

This project is to explore the theoretical and practical issues of the on-line training and real-time applications of a new Hopfield-based dynamic neural network (HDNN) which is used as a system identifier and a direct adaptive controller for nonlinear systems. It is well known that system identification process has been one of central parts in various control researches. Recent research results show that neural network techniques, whether static or dynamic neural networks, are very effective to identify a wide class of complex nonlinear systems even with incomplete model information. However, static neural networks (SNNs) are unable to represent dynamic system mapping without the aid of tapped delay and hence have limited applicability on system identification; on the other hand, most of dynamic neural networks (DNNs) for system identification involve a learning process which has no guarantee for convergence. Considering the drawbacks of SNNs and DNNs on system identification in previous researches, we will propose a new HDNN to perform nonlinear system identification. Convergent analysis will be performed by the Lyapunov-like criterion to guarantee the error convergence during identification. Therefore, the weighting factors of the proposed neural network can be adjusted by the Lyapunov approach to satisfy the convergent criterion. Both training algorithm and robustness analysis will be performed in the first year by extensive computer simulations. The effect of the self-feedback loops of the HDNN will be investigated to enhance the performance of the HDNN. In the second year, the hardware implementation of the trained HDNN will be realized to identify an inverted pendulum system and a ball-and-beam system. In the third year, we will try to propose a direct adaptive control scheme using HDNN. We eliminate the need of system identification process in the proposed control scheme to reduce the complexity of the whole system and hence improve the feasibility of hardware implementation. In this control scheme, the HDNN is used to approximate an ideal controller, and the weighting factors will be on-line tuned by the adaptive laws in the Lyapunov sense so that the stability of the closed-loop system can be guaranteed. We will first examine the correctness of the proposed direct adaptive control scheme by computer simulation. Then, the hardware implementation of the HDNN controller will be realized to control a chaotic circuit to show its effectiveness.