多约束纯反馈非线性系统鲁棒自适应抗干扰控制

Adaptive robust anti-disturbance control for pure feedback nonlinear systems with multiple constraints

针对一类具有未知干扰和多约束的不确定纯反馈非线性系统,提出一种基于干扰观测器的鲁棒自适应抗干扰控制方案.该方法首先基于Butterworth低通滤波器和径向基神经网络设计非线性干扰观测器以实现对系统未知非线性函数和复合扰动的在线精确逼近,并消除"代数环"问题.其次,为确保系统在状态受限、预设性能和输入饱和等多重约束的综合影响下能够对期望轨迹进行稳定跟踪,构造了一种新型的障碍Lyapunov函数,结合辅助有界函数、Nussbaum函数和一阶滑模微分器设计Backstepping控制器,并通过Lyapunov稳定理论分析闭环系统稳定性.最后,仿真结果验证了所提控制方法的有效性.

To solve the control problem for a class of uncertain pure feedback nonlinear systems subjected to external disturbances and multiple constraints, an adaptive robust control methodology is proposed based on a disturbance observer. To handle unknown nonlinearity and external unknown disturbances, a nonlinear disturbance observer is constructed based on a radial basis function neural network, which uses a Butterworth low-pass filter to remove the algebraic loop problem. Then, to guarantee that the system can stably track the desired trajectory under the state constraints, input saturation, and prescribed tracking performance constraints,we developed a novel barrier Lyapunov function and a backstepping controller that combines an auxiliary bounded function, a Nussbaum function, and a first-order sliding-mode differentiator. Subsequently, the stability of the closed-loop system is rigorously proved by Lyapunov analysis. Finally, simulations are conducted to demonstrate the effectiveness of the proposed approach.