基于T-S模型的非线性系统非脆弱极小极大控制

研究一类非线性离散系统的鲁棒非脆弱极小极大控制问题.针对含有不确定项的非线性离散系统,构造T-S模型,引入参数不确定项,使得模糊模型能够更精确逼近原系统.考虑系统和控制器同时含有不确定性,利用线性矩阵不等式(LMI)处理方法和Lyapunov稳定性理论,设计鲁棒且非脆弱的控制器.考虑不确定性使得性能指标最大的情形,得到极小极大鲁棒非脆弱控制器存在的充分条件.引入凸优化算法,求解使闭环系统渐近稳定且性能指标上界最小的最优极小极大鲁棒控制器的参数.最后以著名的truck-trailer模型为例的仿真结果表明所设计的控制器具有良好的鲁棒性和非脆弱性.

Non-fragile minimax control of nonlinear systems based on T-S model

To deal with the robust and non-fragile minimax control problem for uncertain nonlinear discrete systems, we construct a T-S model including the parametric uncertainty terms of the nonlinear systems to give a better approximation to the original system. The sufficient conditions for the existence of robust and non-fragile minimax control are derived in the sense of Lyapunov asymptotic stability and are formulated in the format of linear matrix inequalities (LMIs). The convex optimization algorithm is used to determine the minimal upper bound of the performance cost and the parameters of optimal minimax controller. The closed-loop system is asymptotically stable under the worst disturbances and the greatest uncertainty. An illustrative example of truck-trailer shows a good robust and non-fragile performance of the designed controller.