【作者】 董久祥；

【导师】 杨光红；

【作者基本信息】 东北大学 ， 导航、制导与控制， 2009， 博士

【摘要】 随着科学的日益发展,我们对控制系统的要求越来越高,系统也日趋复杂,并且由于被控对象或过程的非线性、较大的随机干扰、各种不确定性等因素的影响经常导致难以建立满足控制要求的数学模型。对于这样的系统,传统的控制理论则很难被应用。而模糊控制技术由于其自身具有人类自然语言的定性描述的特点,能够有效地克服这些困难实现对被控对象的控制。特别地,基于T-S模糊模型的非线性系统的稳定性分析和控制器设计的研究近年来吸引了广大学者和专家的兴趣。许多重要的进步已经被取得。但是由于模糊控制系统固有的非线性特性,探求更加有效的模糊系统的稳定性分析和控制器设计条件仍然是模糊控制理论研究的一项重要的任务。本论文在总结前人工作的基础上,进一步深入地研究了T-S模糊系统的若干控制问题。具体如下：针对连续T-S模糊系统,使用模糊隶属度函数的性质,提出了新的线性矩阵不等式(LMI)技术,它能引入比已有方法更多的LMI变量,进而获得了具有更少保守性的稳定性分析和控制器设计条件；针对离散T-S模糊系统，通过使用输出矩阵核空间的性质,给出了新的基于LMI的方法来设计H∞静态输出反馈控制器,并出示了所提出方法能给出比已有方法更少保守性的解；首次提出了T-S模糊系统的一类新的控制策略,即,切换PDC控制策略,并给出了基于LMI的切换PDC控制器设计方法,减少了目前控制器设计方法的保守性；针对已有复杂的非线性系统的T-S模糊模型具有太多模糊规则导致控制器难以设计和实施的困难,给出了一类由局部非线性子模型构成的T-S模糊模型的建模方法及相应的控制器设计技术。所提出的方法能减少传统方法的计算负担并构造出具有更少模糊规则的控制器,而且它也可以给出更少保守性的解；针对模糊奇异摄动系统,提出一类能够改善奇异摄动参数的上界新的控制器设计技术,进而克服了已有奇异摄动系统控制器设计技术无法改善奇异摄动参数的上界的缺点；此外,针对模糊马尔可夫跳变系统,给出了新的基于LMI的模型独立控制器的设计条件,新的条件中引入了比已有方法更多的LMI变量,于是增加了算法的自由度,进而能够给出更少保守性的解。本文的主要研究内容如下：第一章系统地分析和总结了模糊控制理论研究领域的发展现状。第二章针对连续T-S模糊系统,使用模糊Lyapunov函数,通过探求一个可以引入更多的变量新的LMI技术获得了一个带有线性搜索的基于LMI的控制器设计方法。与已有的方法相比,更多的松弛变量增加了算法的自由度,于是可以得到更少保守性的解。进一步通过数值例子验证了该方法的有效性。针对离散T-S模糊系统,首次利用系统输出矩阵的核空间的性质引入带有下三角结构的参数依赖的松弛变量,给出了基于LMI的静态输出反馈控制器设计条件。与已有的静态输出反馈控制器设计技术相比,所提出的方法避免了对Lyapunov矩阵的约束,可以给出更少保守性的设计。仿真算例出示了所提出方法的有效性。第三章通过深入分析模糊系统的特点,首次提出了一类依赖于模糊隶属度函数值进行切换的控制策略,即,切换PDC控制策略。本章分别给出了连续和离散T-S模糊系统的基于LMI的切换PDC控制器设计方法。所提出的方法包含了已有的PDC控制器设计方法和切换线性控制器设计方法,因此它能给出更少保守性的结果。仿真算例进一步表明本章所提出方法相对于已有方法的优越性。第四章考虑了复杂非线性系统的模糊控制器设计问题。这样的系统的T-S模糊模型通常有大量模糊规则,于是基于这个模糊模型的控制器设计方法经常有非常大的计算负担以至于可能无法得到可行的结果,即使能得到可行的结果,但因为所设计的控制器具有大量的模糊规则而不便于工程实施。为了克服这一困难,本章首次提出带有局部非线性子模型的T-S模糊模型的建模技术并给出了相应的控制器设计方法。与已有的方法相比,新的方法能获得更少模糊规则的控制器并且有更少的计算负担。特别地,非线性子模型的使用可以保留非线性系统重要的非线性属性,于是它也能够给出更少保守性的解。仿真算例进一步验证了所提出方法的有效性。第五章考虑了奇异摄动T-S模糊系统的控制器设计和奇异参数摄动界的估计问题。针对连续奇异摄动T-S模糊系统,首次给出了能够通过设计控制器来改善奇异摄动参数上界的控制器设计技术。针对离散奇异摄动系统提出了两个仅使用慢状态信息的H∞控制器设计的LMI条件,其中之一可以通过设计控制器来改善奇异摄动参数上界。特别地,这两个条件都移除了已有的基于Riccati方程或不等式方法只能应用于满足正则性的系统的约束。仿真算例进一步表明所提出优化方法的有效性。第六章针对连续马尔可夫跳变系统,使用随机Lyapunov函数方法并通过新的LMI技术引入了松弛变量分离系统矩阵和随机Lyapunov矩阵,给出了基于LMI的模型独立的控制器设计条件。与已有的方法相比,所提出的方法引入了更多的LMI变量,进而能给出更少保守性的解。这一事实将通过理论证明和仿真算例进一步验证。最后对全文所做的工作进行了总结,并指明了下一步研究的方向。更多还原

【Abstract】 With the developments of the science, we have more requirements for control sys-tems and the control systems are more complex. The controlled object or process often is nonlinear, subject to some random disturbances and uncertainties, so that its mathe-matical model, which can satisfy our demands, is not available. For the control system, the conventional control theory is not applicable. However, the fuzzy control techniques with a property of human language can overcome the difficulties. In particular, stability analysis and control synthesis of nonlinear systems described by T-S fuzzy models appeal many researchers’interest and many important progresses have been achieved. Due to the inherent nonlinearities of T-S fuzzy systems, it is still a very important task to exploit more effective conditions for stability analysis and control synthesis.Based on the previous work of other researchers, this thesis further studies some control problems of T-S fuzzy systems, which are given as follows:By using the prop-erties of fuzzy membership functions, a new LMI technique, which can introduce more LMI variables than the existing ones, is proposed. Further, by the new technique, the conditions with less conservatism are given for stability analysis and control synthesis for continuous-time T-S fuzzy systems; By using the properties of the null space of sys-tem output matrix, a new LMI-based condition for designing H^ static output feedback controllers for discrete-time T-S fuzzy systems is given. In contrast to the existing ap-proaches, the new one removes the constraint on the structure of Lyapunov matrices, then it can gives less conservative results; A new control scheme for T-S fuzzy systems, i.e., switching PDC control scheme, is proposed for the first time. The corresponding LMI-based control design approaches are given. The proposed approaches can be reduced to the PDC controller design methods or switching linear controller design methods under some additional constraints, then they can give less conservative results; A new type of T-S fuzzy models, which consist of local nonlinear subsystems, is constructed for a class of nonlinear systems with strong nonlinearities, and the corresponding conditions for design-ing controllers are given. The proposed approach can overcome the difficulty of designing controllers based on the conventional T-S fuzzy models due to too many fuzzy rules in the model. It can reduce the computational burden and give less conservative results; A controller design method for singularly perturbed fuzzy systems, which can improve the upper bound of the singular perturbation parameter by designing controllers, is given. The proposed method overcomes the difficulty that the existing approaches cannot improve the upper bound of the singular perturbation parameter by designing controllers. Moreover, a new condition for designing mode-independent controllers for Markovian jump fuzzy systems is given. More slack variables are introduced in the proposed condition, then the proposed method is more flexible in the freedom and can given less conservative results than the existing ones.The considered main issues are given as follows:In Chapter 1, the background and the development of fuzzy control are summarized and analyzed.In Chapter 2, a new LMI technique, which can introduce more variables, is ex-ploited, then an LMI-based method with a linear search for designing fuzzy controllers for continuous-time T-S fuzzy systems is obtained. In contrast to the existing approaches, the new one is more flexible in the freedom due to more slack variables, therefore, it can give less conservative results. Numerical examples are further given for showing the effectiveness of the proposed approach. Moreover, by using the properties of the null space of output matrices, a parameter-dependent slack variable with lower-triangular structure is introduced, then a new method for designing static output feedback controllers is obtained. In contrast to the existing approaches, the proposed method can remove the constraint on Lyapunov matrices and give less conservative results. Numerical examples validate the effectiveness of the proposed approachIn Chapter 3. by analyzing the properties of fuzzy systems, a new control scheme, i.e., switching PDC control scheme, is proposed for the first time. LMI-based condi-tions for designing switching PDC controllers are given respectively for continuous and discrete-time T-S fuzzy systems. The existing PDC controller design methods or switch-ing linear controller design methods can be considered as a special case of the new control scheme. Therefore, the proposed method can give less conservative results than the ex-isting ones. Numerical examples are given to show the effectiveness of the proposed approaches.In Chapter 4, fuzzy controller design problems of a class of nonlinear systems with complex nonlinearities are considered. The T-S fuzzy models of the class of nonlinear systems are of very many fuzzy rules, so that the methods for designing controller have heavy computational burden or cannot get a feasible solution. Moreover, the obtained controllers are not convenient for implementing in engineering. In order to overcome the difficulty, a new type of T-S fuzzy models with local nonlinear subsystems are proposed and the corresponding control synthesis techniques are given. In contrast to the existing approaches, the proposed one can obtain a fuzzy controller with less fuzzy rules and has less computational burden. In particular, some important properties of nonlinear systems can be reserved due to the use of the nonlinear subsystems, then it also can give less conservative results. The effectiveness of the proposed method is validated by numerical examples.In Chapter 5, the problems of the controller design, and the estimation of the up-per bound of singular perturbation parameter of singularly perturbed fuzzy systems are considered. A controller design method with improving the upper bound of the singular perturbation parameter is given for the first time for continuous-time singularly perturbed fuzzy systems. Moreover, two LMI-based conditions for designing Hx controllers only by slow state information for discrete-time singularly perturbed fuzzy systems are pro-posed, where one of them can improve the upper of singular perturbation parameter by designing controllers. Both of them remove the constraint on Riccati equation or inequal-ity approaches, where the systems have to satisfy the regularity. The effectiveness of the proposed methods are validated by numerical examples.In Chapter 6, based on stochastic Lyapunov functions and by introducing slack vari-ables for separating the system matrix and Lyapunov matrix, an LMI-based condition for designing mode-independent controllers is given for Markovian jump fuzzy systems. In contrast to the existing approach, the proposed method is of more LMI variables, then can give less conservative results. Numerical examples further show the effectiveness of the proposed method.Finally, the results of the dissertation are summarized and further research topics are pointed out.更多还原