基于T-S模糊模型切換非線性系統(tǒng)的穩(wěn)定性分析與控制
發(fā)布時間：2018-10-08 18:52
【摘要】：研究切換非線性系統(tǒng)控制過程時,既要選取恰當?shù)那袚Q信號又要保證切換時間足夠快。這些都為處理切換非線性系統(tǒng)的穩(wěn)定性分析與控制帶了難度。再者,實際切換非線性系統(tǒng)中存在大量的不確定性參數(shù),使得系統(tǒng)的精確控制更具有挑戰(zhàn)性。二型模糊系統(tǒng)在處理系統(tǒng)含有不確定性參數(shù)的問題時,具有明顯超過一型模糊系統(tǒng)的性能表現(xiàn)。因此,本文圍繞解決含有部分不穩(wěn)定的切換非線性系統(tǒng),提出合適的切換規(guī)則,通過Takagi-Sugeno(T-S)模糊模型、區(qū)間二型(IT2)T-S模糊模型逼近非線性系統(tǒng),使其局部線性化。再利用IT2 T-S模糊模型隸屬度函數(shù)的特性,來降低系統(tǒng)的保守性等內容進行以下展開。針對含有部分不穩(wěn)定的切換非線性系統(tǒng),利用T-S模糊模型逼近非線性系統(tǒng),通過提出的新穎的MDADT切換信號-類選擇切換信號以保證切換系統(tǒng)的穩(wěn)性;對于含有不確定性參數(shù)的切換非線性系統(tǒng),IT2 T-S模糊模型展現(xiàn)了更好的處理結果,通過改善的ADT方法,經過一系列LMIs的等價變換,得到切換IT2 T-S模糊系統(tǒng)是漸進穩(wěn)定的;再次針對含有不確定性參數(shù)的切換非線性系統(tǒng),為了得到更小ADT,采用了擴展的切換信號,通過延遲切換控制保證這些子系統(tǒng)鎮(zhèn)定,同時選取恰當?shù)腎T2 T-S模糊模型上、下限隸屬度函數(shù)的權重系數(shù),來降低切換系統(tǒng)的保守性。最后,根據(jù)已有的條件和技術進行仿真實驗,證明了所研究的基于T-S模糊模型切換非線性系統(tǒng)的穩(wěn)定性分析與控制方法的有效性。
[Abstract]:When studying the control process of switched nonlinear systems, it is necessary to select appropriate switching signals and ensure that the switching time is fast enough. All these make it difficult to deal with the stability analysis and control of switched nonlinear systems. Furthermore, there are a large number of uncertain parameters in switched nonlinear systems, which make the precise control of the system more challenging. The performance of a type II fuzzy system is obviously better than that of a type of fuzzy system when it deals with the problem with uncertain parameters. Therefore, in this paper, a suitable switching rule is proposed for solving switched nonlinear systems with partial instability. The nonlinear systems are approximated by Takagi-Sugeno (T-S) fuzzy model and interval 2 (IT2) T-S fuzzy model to make it locally linearized. Using the characteristic of membership function of IT2 T-S fuzzy model to reduce the conservatism of the system, the following expansion is carried out. For switched nonlinear systems with partial instability, the T-S fuzzy model is used to approximate the nonlinear systems, and the stability of switched systems is ensured by a novel MDADT switching signal-class selective switching signal. For switched nonlinear systems with uncertain parameters, the IT2T-S fuzzy model shows better results. By the improved ADT method and a series of equivalent LMIs transformations, the switched IT2 T-S fuzzy systems are asymptotically stable. Thirdly, for switched nonlinear systems with uncertain parameters, in order to obtain a smaller ADT, with extended switching signals, the stabilization of these subsystems is ensured by delay switching control, and the appropriate IT2 T-S fuzzy model is selected at the same time. The weight coefficient of the lower limit membership function is used to reduce the conservatism of switched systems. Finally, according to the existing conditions and techniques, the simulation results show that the proposed stability analysis and control method based on T-S fuzzy model switching nonlinear system is effective.
【學位授予單位】：渤海大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：TP13
[Abstract]:When studying the control process of switched nonlinear systems, it is necessary to select appropriate switching signals and ensure that the switching time is fast enough. All these make it difficult to deal with the stability analysis and control of switched nonlinear systems. Furthermore, there are a large number of uncertain parameters in switched nonlinear systems, which make the precise control of the system more challenging. The performance of a type II fuzzy system is obviously better than that of a type of fuzzy system when it deals with the problem with uncertain parameters. Therefore, in this paper, a suitable switching rule is proposed for solving switched nonlinear systems with partial instability. The nonlinear systems are approximated by Takagi-Sugeno (T-S) fuzzy model and interval 2 (IT2) T-S fuzzy model to make it locally linearized. Using the characteristic of membership function of IT2 T-S fuzzy model to reduce the conservatism of the system, the following expansion is carried out. For switched nonlinear systems with partial instability, the T-S fuzzy model is used to approximate the nonlinear systems, and the stability of switched systems is ensured by a novel MDADT switching signal-class selective switching signal. For switched nonlinear systems with uncertain parameters, the IT2T-S fuzzy model shows better results. By the improved ADT method and a series of equivalent LMIs transformations, the switched IT2 T-S fuzzy systems are asymptotically stable. Thirdly, for switched nonlinear systems with uncertain parameters, in order to obtain a smaller ADT, with extended switching signals, the stabilization of these subsystems is ensured by delay switching control, and the appropriate IT2 T-S fuzzy model is selected at the same time. The weight coefficient of the lower limit membership function is used to reduce the conservatism of switched systems. Finally, according to the existing conditions and techniques, the simulation results show that the proposed stability analysis and control method based on T-S fuzzy model switching nonlinear system is effective.
【學位授予單位】：渤海大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：TP13
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