Robust Control for Uncertain Fuzzy Nonlinear Time-Delay Systems with Application to Practical Systems

本课题主要研究具有时滞和不确定性的Takagi-Sugeno模糊系统的系统分析与综合。首先，对一类具有定常时滞的名义模糊系统进行了稳定性分析。一般情况下，由于所考虑的系统是非线性时滞系统，很难得到系统稳定的充分必要条件。因此，将原非线性时滞系统转化为模糊时滞系统，并通过线性矩阵不等式得到模糊时滞系统的稳定性条件作为充分条件。在稳定性条件的推导中，采用莱布尼兹-牛顿公式和自由加权矩阵法来降低稳定性条件下的保守性。将具有不确定矩阵的模糊时滞系统的稳定条件推广为鲁棒稳定条件。基于这些稳定条件，设计了标称模糊时滞系统的镇定控制器和不确定模糊时滞系统的鲁棒镇定控制器。对于一类系统，不仅要考虑具有离散延迟的系统，而且要考虑具有离散和分布延迟的系统。对于时间延迟，不仅考虑定常延迟，还考虑时变延迟。此外，还提出了一种能够衰减系统干扰和测量噪声的Hoc控制器设计。给出了在模糊时滞系统控制设计中起重要作用的自适应滤波器。最后，将上述理论设计应用到实际系统中。通过数值仿真，将所设计的控制器应用于倒立摆、直升机等实际系统。结果表明，该控制器在实际系统中运行良好。

In this research project, system analysis and synthesis of Takagi-Sugeno fuzzy systems with time-delay and uncertainties were concerned. First, stability analysis on a nominal fuzzy system with time-invariant delay was considered. In general, it is difficult to obtain a necessary and sufficient stability condition for the system because a system under consideration is a nonlinear time-delay system. Hence, an original nonlinear time-delay system was transformed into a fuzzy time-delay system and a stability condition for a fuzzy time-delay system was obtained as a sufficient condition via linear matrix inequality. In the derivation of stability condition, Leibniz-Newton formula and free weighting matrix method were employed to reduce the conservatism in stability condition. A stability condition was extended to a robust stability condition for a fuzzy time-delay system with uncertainties in system matrices. Based on such stability conditions, stabilizing controller for a nominal fuzzy time-delay system and robust stabilizing controller for an uncertain fuzzy time-delay system were designed. As for a class of systems, not only systems with discrete delays but also systems with discrete and distributed delay are concerned. As for time delays, not only time-invariant delays but also time-varying delays were considered. Moreover, an Hoc controller design which attenuate system disturbances and measurement noises was proposed. An Hoc filter which plays an important role in control design for a fuzzy time-delay system was also given. Finally, the above theoretical design was applied to practical systems. After making numerical simulations, controllers designed as above were applied to practical systems such as inverted pendulum and helicopter. It was found that such controllers worked well for those practical systems.