摘要
近年来,作为智能控制研究领域的一个重要分支,非线性系统的模糊自适应控制引起了越来越多学者的重视。本文就此领域的相关问题展开系列研究,主要研究了不确定非线性系统的控制器与观测器设计问题。以李亚普诺夫(Lyapunov)稳定、输入到状态稳定(ISS)、小增益定理、自适应控制、模糊逼近等理论为基础对闭环控制系统进行设计与分析。主要工作如下:
首先,对一类不确定非线性系统,利用H∞控制技术和T-S模糊系统,在状态不完全可测的情况下,提出了一种基于观测器的直接自适应模糊控制方法。通过引入最优逼近误差补偿项,取消了最优逼近误差平方可积的假设条件。基于Lyapunov稳定理论,证明了闭环自适应模糊系统半全局一致终结有界,且跟踪误差渐近收敛到零。
其次,对一类状态不完全可测的非仿射不确定非线性系统,利用泰勒展开方法和隐函数定理把系统转化为增益函数未知的不确定非线性系统,结合H∞控制技术和I型模糊系统,提出一种基于观测器的直接自适应模糊控制方法。该方法不仅取消了最优逼近误差平方可积的假设条件,而且获得了良好的跟踪性能。基于Lyapunov稳定理论,证明了闭环自适应模糊系统半全局一致终结有界,且跟踪误差渐近收敛到零。
再次,对一类未知常数增益的不确定非线性系统,将输入到状态稳定理论(ISS)、小增益定理相结合,在状态不完全可测的情况下,提出一种基于Luenberger观测器的自适应模糊控制的新方法。理论分析证明了闭环系统半全局一致终结有界,只有两个参数需要在线调节,同时避免了在一些自适应控制中由于采用线性反馈技术而可能引起的控制器的奇异问题。
最后,对一类状态不完全可测且增益函数未知的不确定非线性系统,利用输入到状态稳定理论(ISS)、小增益定理,提出了一种基于高增益观测器的自适应模糊控制的新方法。该方法取消了基于普通观测器设计控制器时要求待观测量和观测量有界的假设条件。理论分析证明了闭环系统半全局一致终结有界,调节参数始终只有两个。通过本文的研究,较好地解决了一些不确定非线性系统的模糊自适应控制问题。仿真结果表明所提控制方案的有效性。
As an important branch in the field of intelligent control, fuzzy adaptive control for nonlinear systems has been received more and more attention in recent years. Some correlative issues in this area are studied in this paper. The main issues are the controller and observer design problems of uncertain nonlinear systems. The design and analysis procedure is based on a series of control theories, which include Lyapunov stability theory, input-to-state stability theory, small-gain theorem, adaptive control theory, fuzzy approximate theory, and so on. The main work in this paper is summarized as follows.
Firstly, using H∞control technique and T-S fuzzy systems, an observer-based direct adaptive fuzzy control is developed for a class of uncertain nonlinear systems under the condition that not all of the state variables of the systems is available. By introducing the adaptive compensation term of the optimal approximation error, the square integrable condition of the approximation error is avoided. Based on Lyapunov stability theorem, the closed-loop adaptive fuzzy control system is proved to be semi-globally uniformly ultimately bounded, with the tracking error converging to zero asymptotically.
Secondly, an observer-based direct adaptive fuzzy control is developed for a class of nonaffine uncertain nonlinear systems under the condition that not all of the state variables of the systems is available. Using Taylor expansion method and connotative function theorem, the controlled object is changed into a class of uncertain nonlinear systems with unknown gain function. The observer-based adaptive fuzzy controller is gained by use of H∞control technique and fuzzy systems. Not only the square integrable condition of the approximation error is avoided, but also the good tracking performance is obtained. Based on Lyapunov stability theorem, the closed-loop adaptive fuzzy control system is proved to be semi-globally uniformly ultimately bounded, with the tracking error converging to zero asymptotically.
Thirdly, using ISS theory, small-gain theorem and T-S type fuzzy logic systems, which are used to approximate the uncertain system function, a Luenberger observer-based direct robust adaptive fuzzy control is developed for a class of nonlinear systems with unknown constant gain under the condition that not all of the state variables of the systems are available. The resulting closed-loop system is proved to be semi-globally uniformly ultimately bounded. In addition, the controller singularity problem commonly encountered in adaptive feedback linearization control can be avoided and only two learning parameters need to be adjusted on line.
Lastly, using ISS theory, small-gain theorem and T-S type fuzzy logic systems, which are used to approximate the uncertain system function, a high-gain observer-based robust adaptive fuzzy control is developed for a class of nonlinear systems with uncertain gain function under the condition that not all of the state variables of the systems is available. The supposed condition that the unavailable state and the observed state of the systems have upper bounds usually encountered in adaptive fuzzy control which is based on common observer is avoided. The resulting closed-loop system is proved to be semi-globally uniformly ultimately bounded. In addition, the controller singularity problem commonly encountered in adaptive feedback linearization control can be avoided and only two learning parameters need to be adjusted on line. Simulation results show the effectiveness of the control scheme.
Through the research in this paper, some fuzzy adaptive control problems for uncertain nonlinear systems have been properly solved. Numerical simulation experiments of these control schemes demonstrate their effectiveness.
引文
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