一类时滞非线性系统的自适应控制器设计

Adaptive Controller Design for a Class of Time-delay Nonlinear Systems

针对一类带有扰动的未知时滞非线性系统,将未知的非线性函数表示成新的表达式,利用反步方法设计了一种鲁棒自适应控制器。首先构造一种新的LyapunovKrasovskii泛函,有效补偿了未知时滞的不确定性,使得控制器的设计不存在未知时滞项。然后引入一种合适的偶函数,解决了控制器的奇异性问题。最后利用Lyapunov直接方法,证明了设计的控制器能保证闭环系统全局一致最终有界。通过仿真实例验证了所设计的自适应控制器的有效性。

By using the backstepping design method and turning the unknown nonlinear function into a new expression, a robust adaptive controller was proposed for a class of unknown time-delay nonlinear systems with disturbance. Firstly, a new Lyapunov-Krasovskii functional was used to compensate the uncertainty of unknown time-delay. And there is no unknown time-delay term in the controller design. Then an appropriate even function was introduced to avoid the controller singularity problems. Finally, it was proved that the global uniform ultimate boundedness of all the signals in the closed-loop systems was guaranteed by the Lyapunov direct method. The effectiveness of the designed controller was illustrated by a simulation case.