基于模糊双曲模型的混合H_2/H_∞控制

Design of Mixed H_2/H_∞ Controller Based on Fuzzy Hyperbolic Model

针对一类离散非线性系统,提出一种基于模糊双曲模型(FHM)的多目标控制器设计方法.利用模糊双曲模型来表述一类非线性系统,建立基于模糊双曲模型的控制器.该控制器本质上是一种模糊控制器,也是具有饱和特性的非线性反馈控制器.使用LMI方法设计该控制器以保证闭环系统是渐近稳定的,并且可以通过求解一个基于LMI的优化问题,得到次优的控制器增益矩阵,使得闭环系统同时满足H2性能指标上界最小和H∞范数界γ.仿真结果表明,该方法是有效的.

Based on fuzzy hyperbolic model （FILM）, a multiple-objective controller design method is presented for a class of discrete-time nonlinear systems, where the FHM is refers to the descriptive definition of a class of nonlinear systems and the architecture of the FHM controller. This controller is essentially a fuzzy controller and also a nonlinear feedback controller featured with saturation. Design with the linear matrix inequality （LMI）, the controller can guarantee the asymptotic stability of a closed-loop system and, a suboptimal gain matrix of the controller can be obtained by .solving an LMI-based optimization problem to enable the closed-loop system to satisfy simultaneously both the upper bound of H2 performance index and H∞ norm bound γ. Simulation results showed the validity of the design method proposed.