非線性不確定系統之即時智慧型適應性控制

Abstract

本篇論文提出一種非線性不確定系統之即時智慧型非直接適應性控制理論。此理論最主要的功能是利用Takagi-Sugeno (TS)模糊類神經網路，即時將非線性系統線性化。再依據所學得的線性化系統來設計控制器，以達到使非線性系統穩定追蹤的目的。在TS模糊類神經網路之學習上，我們採用[13]所提出之兩層類神經網路最佳學習法，將此法應用在TS模糊類神經網路的學習上。因此我們不但可以保證TS模糊類神經網路學習的收斂性，而且也可以保證其收斂速率是最快的。除此之外，我們為了使TS模糊類神經網路收斂的更有效率，本論文採用最小誤差法(least squared method)[1]來估測TS模糊類神經網路之初始權重參數。此法所得之初始權重參數，可使TS模糊類神經網路收斂致全域最小點(global minimum)。在控制器設計方面，我們採用狀態回授追蹤控制的架構，再依據所學得的線性模型來設計控制器的參數，使非線性系統作穩定追蹤。本論文以質量-彈簧-阻尼器( Mass-Spring-Damper)、倒單擺(Inverted Pendulum)和混沌電路(Chua’s Chaotic Circuit)來作範例來驗證所提出之控制器之可行性及實用性。

A new approach for on-line intelligent indirect adaptive control of uncertain nonlinear systems is explored in this thesis using optimally trained Takagi-Sugeno (TS)-type fuzzy models. It is a common practice to assume that the uncertain nonlinear system can possess a linearized TS-type fuzzy model at any time instant. The linearized TS-type fuzzy model should be different at different time instants. The dynamical optimal learning rule can be adopted to update the linearized TS-type fuzzy model to guarantee the convergence of on-line training process. Also the initialization of the linearized TS-type fuzzy model is very important to speed-up the convergence rate. This will be based on the least-squared identification. It must be emphasized that once the linearized TS-type fuzzy model of the uncertain nonlinear system is obtained in real-time environment, the on-line adaptive controller can be easily designed to accomplish the design specifications, i.e., stabilizing the unknown nonlinear system, tracking of a reference signal, …, etc. A simplified tracking controller is also proposed to perform the tracking of a reference signal for the unknown nonlinear system. Two nonlinear systems, i.e., mass-spring-damper, inverted pendulum system, and Chua’s chaotic circuit are fully illustrated to track sinusoidal signals. The resulting on-line indirect adaptive controller shows excellent results.