带有多个离散和分布时滞的不确定系统的鲁棒自适应控制

对于带有多个离散和分布时滞且有外部干扰的不确定线性系统提出一类鲁棒自适应控制方案.系统的不确定性是范数有界的未知连续函数,外部干扰是扇形有界的.分2步证明其结论:首先用线性矩阵不等式方法说明状态反馈控制可以保证系统的确定部分的稳定性;其次由于系统的不确定部分的上界未知,用自适应的方法来估计上界的值;利用径向基函数神经网络来估计关于状态的未知连续函数;最终证明了在结合状态反馈和自适应神经网络控制的复合控制律作用下闭环系统是渐近稳定的.然后,在第一步基础上,要求系统满足2个不等式条件,设计相应的控制律参数,用Lyapunov-Krasovskii泛函方法证明了闭环系统是指数稳定的.

Robust adaptive control for uncertain systems with multiple discrete and distributed delays

A robust adaptive control scheme is proposed for the stabilization of uncertain linear systems with multiple discrete and distributed delays and bounded perturbations.The uncertainty is assumed to be unknown continuous function with norm-bounded restriction.The perturbation is sector-bounded.The proof is presented in two steps.Step 1,linear matrix inequality(LMI) method is utilized to demonstrate that the certain part of the system can be stabilized by state feedback control.Because the upper boundary of the uncertainty of the system is unknown,the adaptive method is employed to estimate the upper boundary.The unkown continuous function about state is estimated by radius basis function neural networks.Together with the controller which is composed of state feedback,neural networks and adaptive control,the close-loop system is proved to be asymptotically stable.Step 2,on the base of step 1,two inequality conditions about the system are required.The parameter of control law is correspondingly designed.By Lyapunov-Krasovskii functional method,the exponential stability of the close-loop system is proved.