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H_∞ fuzzy adaptive tracking control design for nonlinear systems with output delays

机译：输出非线性系统的H_∞模糊自适应跟踪控制设计。

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摘要

In this study, we develop fuzzy adaptive tracking control via two-layer fuzzy observers, variable structure systems (VSS), and H_∞ control algorithm for nonlinear systems with plant uncertainties, output delays, and external disturbances. The Takagi-Sugeno fuzzy dynamic model with adaptation capability is used to approximate the nonlinear system. When the system states are not available, the states estimated from two-layer fuzzy observers combined with VSS are used to develop the fuzzy adaptive controller. In the first layer, the output delays are partitioned into m + 1 equal time intervals to construct the same number of fuzzy observers. The output delayed states in each time interval are used as the premise variables in the IF-THEN rules. The second layer of the fuzzy observers uses output delayed error states as its linguistic variables and it is defuzzified from the first layer. Next, we develop a fuzzy adaptive controller to overcome the nonlinearities, output delayed states, and external disturbances such that H_∞ tracking performance is achieved. The Lyapunov criterion and linear matrix inequalities are used to derive the controller. In the present study, our previous method is extended to handle a class of uncertain nonlinear systems with output delays and external disturbances, which is achieved using robust VSS and H_∞ control techniques. A magnetic levitation system and inverted pendulum system are used as simulation examples to illustrate the validity and confirm the performance of our proposed scheme.
机译：在这项研究中，我们通过两层模糊观测器，可变结构系统（VSS）和具有工厂不确定性，输出延迟和外部干扰的非线性系统的H_∞控制算法，开发了模糊自适应跟踪控制。具有适应能力的Takagi-Sugeno模糊动力学模型被用来近似非线性系统。当系统状态不可用时，将从结合VSS的两层模糊观测器估计的状态用于开发模糊自适应控制器。在第一层中，将输出延迟划分为m + 1个相等的时间间隔，以构造相同数量的模糊观测器。每个时间间隔中的输出延迟状态在IF-THEN规则中用作前提变量。模糊观察者的第二层使用输出的延迟错误状态作为其语言变量，并且从第一层开始对其进行去模糊处理。接下来，我们开发了一种模糊自适应控制器来克服非线性，输出延迟状态和外部干扰等问题，从而实现H_∞跟踪性能。使用李雅普诺夫准则和线性矩阵不等式推导控制器。在本研究中，我们先前的方法已扩展为处理一类具有输出延迟和外部干扰的不确定非线性系统，这是使用鲁棒的VSS和H_∞控制技术实现的。以磁悬浮系统和倒立摆系统为例，验证了所提方案的有效性和性能。

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