不确定系统混合H2/H∞鲁棒控制的直接迭代LMI方法

设计多胞型不确定系统的控制器时,引入附加变量能够减小设计保守性,但这会使线性矩阵不等式(LMI)的维数大大增加,控制器难以求解.本文阐述了一种基于直接迭代线性矩阵不等式(DILMI)方法的混合H2/H∞鲁棒控制方法.首先借助于仿射二次稳定理论将整个多胞型不确定集合的稳定性问题转化为该集合各顶点的稳定性问题.利用参数依赖Lyapunov方法,给出了一个保证系统鲁棒稳定,并满足混合H2/H∞性能指标的充分条件.随后采用DILMI算法实现了Lyapunov变量和控制增益的解耦,无需引入附加变量就能够求解充分条件中的非凸优化问题.最后,关于F-16多胞型模型的飞行仿真验证了该方法的有效性.

Direct iterative LMI-based approach of mixed H-two/H-infinity robust control for uncertain systems

For the controller design of polytopic uncertain systems, the additional variables method is effective to reduce conservativeness. However, this method makes the dimension of linear matrix inequality (LMI) higher. Motivated by the direct iterative linear matrix inequality (DILMI) approach, a mixed H-two/H-infinity robust control method for polytopic uncertain systems is proposed. First, based on the affine quadratic stability theory, it is proved that the stability of a polytopic uncertain system can be transformed into the stability of the system at vertices of the polytope. In the light of this perspective, a sufficient condition is derived from parameter-dependent Lyapunov approach to guarantee the robust stability and mixed H-two/H-infinity performance of the polytopic uncertain system. Then, a DILMI algorithm is developed for decoupling the Lyapunov variables and the controller gain. The algorithm solves the non-convex optimization problem of the sufficient condition without introducing any additional variables. Finally, simulation results based on the F-16 polytopic model are given to demonstrate the effectiveness of the proposed method.