基于观测器的不确定非线性系统L1自适应控制

针对一类严格块反馈型不确定非线性系统,采用反步设计方法提出了一种新的基于滑模状态观测器的L1自适应控制方案。由于系统状态不完全可测,首先设计滑模观测器对系统状态进行估计,并分析观测器的收敛性,在此基础上,通过反步法得到系统的理想控制律。为了消除反步控制中的“项数膨胀”,引入非线性跟踪微分器来提取理想控制律的微分信号。为提高系统响应的瞬态性能,消除控制输入的高频振荡,引入L1自适应控制对控制律进行改进,通过理论推导证明了闭环系统的稳定性。最后通过数值仿真算例验证了所设计控制方案具有快速的收敛性、良好的跟踪性等期望性能。

L1 adaptive control for a class of uncertain nonlinear systems based on observer

A novel L1 adaptive control strategy based on a sliding mode observer using a back stepping design method for a class of uncertain nonlinear systems in a strict block feedback form is presented. Due to the incompletely observable system states, a sliding mode observer is designed to estimate system states, and the convergence is analyzed. Moreover, the ideal control law is derived through the back stepping method. In order to overcome the “terms explosion” problem, a nonlinear tracking differentiator is used to extract differential signals of virtual control. In order to improve the transient performance of system response and eliminate the high frequency chatter of the control input, the L1 adaptive control is introduced to improve the control laws and the stability of the system is proved. Finally, a numerical simulation is given to demonstrate expected performance of the proposed control scheme.