一类不确定性时滞系统的鲁棒控制器设计

Design of robust controller for a class of uncertain systems with time delay

本文讨论了一类非匹配时滞系统的鲁棒自适应控制和非线性控制问题。所讨论系统包含时滞及不确定性扰动项,且扰动项关于具有未知增益的高阶多项式函数有界而不是关于线性函数有界。利用Lyapunov-Krasovskii方法提出了保证系统渐近稳定的自适应控制器设计方法,相应的控制器是时滞依赖的。并利用Razumikhin引理给出了能使系统一致最终有界稳定的时滞独立的控制器设计方法。

The robust adaptive control and nonlinear state feedback control problems are considered for a class of dynamic systems. The system under study involves time-varying time delay and uncertain perturbations which are bounded by high-order polynomial functions with unknown gains instead of bounded by first-order linear functions and no matching conditions are required. Firstly, a class of adaptive state feedback controllers are presented based on Lyapunov-Krasovskii approach. The controller is dependent on the time delay and can render the closed-loop system asymptotically stable. Then, a nonlinear feedback controller is proposed by applying Razumikhin Lemma. The corresponding controller is independent of the time delay and can guarantee the closed-loop system stable in the sense of uniform ultimate boundedness.