输出受限的不确定非线性系统的自适应固定时间控制

Adaptive fixed-time control for uncertain nonlinear systems with output constraints

针对具有非对称输出约束和外界干扰的不确定非线性系统,提出自适应固定时间反步控制策略.首先,采用非对称障碍Lyapunov函数处理系统的输出约束问题;其次,通过构造固定时间干扰观测器估计外界干扰,设计自适应固定时间滤波器,解决传统反步控制的“计算爆炸”问题,通过自适应律估计虚拟控制输入导数的未知上界;再次,基于Lyapunov稳定性理论证明闭环系统在固定时间内有界稳定且输出保持在约束范围内;最后,通过永磁同步电机的仿真验证所设计的控制策略的有效性.

In this paper,an adaptive fixed time back-stepping control strategy is proposed for an uncertain nonlinear system with asymmetric output constraints and external disturbances.Firstly,an asymmetric barrier Lyapunov function is used to deal with the output constraints of the system.Then,a fixed-time disturbance observer is designed to estimate external disturbances.An adaptive fixed-time filter is designed to solve the problem of“term of explosion”in traditional back-stepping control.An adaptive law is used to estimate the unknown upper bounds of the time derivative of the virtual control input.Moreover,based on the Lyapunov stability theory,it is proved that the bounded stability of the closed-loop system is achieved in fixed time and the output satisfies the constraint conditions.Finally,the effectiveness of the control strategy is verified by an application of a permanent magnet synchronous motor system.