離散區間二型多項式模糊網路系統之強健控制

Robust Control of Discrete-Time Interval Type-2 Polynomial Fuzzy Networked System

劉瑞騰(Rei-Teng Liu)

指導教授 ： 余國瑞

國立中正大學/工學院/機電光工程研究所/碩士(2016年)

摘要

本文提出兩個基於平方和的定理，設計離散區間二型多項式模糊網路強健控制器。此多項式模糊網路系統的模型與控制器均為具有上下界的區間二型模糊集合建立，使前鑑部變數有包含足跡不確定性。其中，第一個定理係考慮網路影響的離散區間二型多項式模糊網路系統的基本穩定定理，經由包含時間延遲與封包丟失的多項式Lyapunov泛函數推導出此系統的穩定條件。定理二則以定理一為基礎發展出同時考慮外部干擾訊號、模式不確定性以及網路影響的離散區間二型多項式模糊網路系統的強健穩定定理，經由包含時間延遲與封包丟失、外部干擾及模式不確定性的多項式Lyapunov泛函數推導出此系統的穩定條件。透過兩個定理可藉由SOSTOOLS求得滿足條件的控制增益，藉由電腦模擬結果顯示，區間二型多項式模糊網路控制器不管與一型多項式模糊網路控制器或區間二型T-S模糊網路控制器比較，皆具有較佳的控制性能。定理一與定理二間的比較，也顯現強健穩定條件對應外部干擾及模式不確定性高度的抑制力。透過自走車的追蹤硬體實驗證實模擬的有效性。

關鍵字

離散區間二型多項式模糊系統 ； 網路控制系統 ； 強健控制

並列摘要

This paper proposes two sum of square-based theorems to design discrete-time interval type 2 polynomial fuzzy networked robust controllers. The models and controllers of the polynomial fuzzy system are both constructed using interval type 2 fuzzy sets, which are bounded by upper and lower membership functions. Theorem 1 is the stability theorem for discrete-time interval type 2 polynomial fuzzy networked systems, which considers the influences of the network. By using the candidate Lyapunov function with networked messages that contain time delays and packet loss, the stability of conditions can be proved. Theorem 2 is the robust stability theorem for discrete-time interval type 2 polynomial fuzzy networked systems, which are developed according to theorem 1 and consider the influences of network, external disturbances, and model uncertainties. By choosing the candidate Lyapunov functional with time delays, packet loss, external disturbances and model uncertainties, robust stability conditions can be proved. The gains that are satisfied with the conditions are solved using sum of square programming through the two theorems. The simulation results indicated an improved performance on interval type 2 polynomial fuzzy networked controllers over the type 1 polynomial fuzzy networked controllers or interval type 2 Takagi–Sugeno fuzzy networked controllers. The comparisons between the gains solved by the two theorems also demonstrated high inhibition on external disturbances and model uncertainties. A wheel mobile robot tracking experiment verified the effectiveness of these simulations.

並列關鍵字

Discrete-time type-2 polynomial fuzzy systems ； networked control ； robust control

參考文獻

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