基于T-S模糊模型切换非线性系统的稳定性分析与控制
发布时间：2018-10-08 18:52
【摘要】：研究切换非线性系统控制过程时,既要选取恰当的切换信号又要保证切换时间足够快。这些都为处理切换非线性系统的稳定性分析与控制带了难度。再者,实际切换非线性系统中存在大量的不确定性参数,使得系统的精确控制更具有挑战性。二型模糊系统在处理系统含有不确定性参数的问题时,具有明显超过一型模糊系统的性能表现。因此,本文围绕解决含有部分不稳定的切换非线性系统,提出合适的切换规则,通过Takagi-Sugeno(T-S)模糊模型、区间二型(IT2)T-S模糊模型逼近非线性系统,使其局部线性化。再利用IT2 T-S模糊模型隶属度函数的特性,来降低系统的保守性等内容进行以下展开。针对含有部分不稳定的切换非线性系统,利用T-S模糊模型逼近非线性系统,通过提出的新颖的MDADT切换信号-类选择切换信号以保证切换系统的稳性;对于含有不确定性参数的切换非线性系统,IT2 T-S模糊模型展现了更好的处理结果,通过改善的ADT方法,经过一系列LMIs的等价变换,得到切换IT2 T-S模糊系统是渐进稳定的;再次针对含有不确定性参数的切换非线性系统,为了得到更小ADT,采用了扩展的切换信号,通过延迟切换控制保证这些子系统镇定,同时选取恰当的IT2 T-S模糊模型上、下限隶属度函数的权重系数,来降低切换系统的保守性。最后,根据已有的条件和技术进行仿真实验,证明了所研究的基于T-S模糊模型切换非线性系统的稳定性分析与控制方法的有效性。
[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.
【学位授予单位】：渤海大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：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.
【学位授予单位】：渤海大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TP13
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