一类不确定非线性系统的自适应鲁棒控制

An Adaptive Robust Controller for a Class of Uncertain Nonlinear Systems

针对一类由非线性微分方程描述的不确定单输入单输出(SISO)系统,提出了一种自适应鲁棒控制算法。设计了一动态滤波器并将其与原系统组成扩展系统,由滤波器求得控制律稳定扩展系统。算法绕开辨识模型参数而是直接估计函数值,加快了控制律的求解。设计了状态误差观测器,用观测器的值构造控制律逼近状态反馈时的控制效果。基于Lyapunov稳定理论分析了扩展系统的渐近稳定性并给出了闭环稳定的充分条件。最后仿真结果验证了算法的有效性和鲁棒性。

A robust adaptive controller is presented for a class of uncertain single - input - single - output （ SI- SO） nonlinear systems described by differential equations. A dynamic filter is designed to solve the control law which can stabilize the expansion system composed of the dynamic filter and original system. The algorithm straight estimates the behavior of unknown function to quicken control law computability without identifying unknown parameters of system. A state error estimator is designed for using its structure control law to approach to the state feedback control. A sufficient condition is obtained after theoretic analysis based on Lyapunov function. The simulation results in the end show that the algorithm is effective and robust.