一类非线性广义系统的有限时间模糊控制

Finite-time Fuzzy Control of a Kind of Nonlinear Descriptor System

研究了一类具有动态干扰的非线性广义系统的有限时间模糊控制问题。给出了模糊有限时间控制器的可解条件以保证闭环系统无脉冲、有限时间有界。所提出方法能消除广义系统的脉冲行为,同时使系统状态在有限时间内保持在预先设定的界内。通过构造一个非奇异矩阵,克服产生不可行矩阵不定式的困难;通过矩阵分解,解决了广义系统自身特征引起的不严格矩阵不等式的问题。结合LMI工具箱的FEASP求解器和GEVP求解器编程仿真,验证了所提出方法的可行性、有效性和简便性。体现了T-S模糊控制方法在研究一类非线性广义系统有限时间控制问题中的应用。就有限时间控制器设计而言,方法简便且易于理解。

This paper investigates the finite-time control problems for a kind of nonlinear descriptor system via a T-S fuzzy model with the dynamic disturbances. The solvable conditions of the fuzzy finite-time controller are proposed to ensure that the closed-loop system is impulse free and finite-time bounded. The obtained method has the ability to eliminate the impulsive behavior of the descriptor system, and the system state remains within prescribed bounds over a fixed finite time interval. A nonsingular matrix is constructed to overcome the difficulties caused by a non-positive definite matrix which will result in an infeasible linear matrix inequality(LMI). The non-strict matrix inequality problem, which is produced inevitably by the characteristic of the descriptor system, is also solved. By combining the FEASP solver with GEVP solver of the LMI toolbox, we perform simulations to validate the obtained method for a nonlinear descriptor system via T-S fuzzy model. It shows the application of the T-S fuzzy method in studying the finite-time control problem for a kind of nonlinear systems. The proposed method is simple and easy to understand for the finite time controller design.