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针对一类具有模型不确定性和未知外界干扰的严反馈非线性MIMO系统,提出一种基于RBF神经网络和反推控制的鲁棒控制律设计方法。应用RBF神经网络在线逼近模型的不确定性,引入低通滤波器消除反推设计方法中由于对虚拟控制反复求导而导致的复杂性问题。同时,在控制律设计中引入一个自适应鲁棒控制项来补偿神经网络逼近误差和未知外界干扰的影响,提高系统的鲁棒性,使整个系统获得更好的跟踪控制性能。基于Lyapunov稳定性定理证明了闭环系统的所有信号半全局一致终结有界;通过适当选择设计参数及初始化误差变量,跟踪误差可收敛到原点的一个任意小邻域内,且跟踪误差的L∞跟踪性能被保证。数值仿真验证了方法的有效性。
For a class of strictly feedback nonlinear MIMO systems with model uncertainties and unknown external disturbances, a robust control law design method based on RBF neural network and backstepping control is proposed. Applying the RBF neural network to approximate the uncertainty of the model online, the low-pass filter is introduced to eliminate the complexity problem caused by repeated derivation of the virtual control. At the same time, an adaptive robust control term is introduced into the control law design to compensate for the influence of approximation error of neural network and unknown external disturbance, and to improve the robustness of the system and achieve better tracking control performance of the whole system. Based on the Lyapunov stability theorem, it is proved that all the signals in the closed-loop system are semi-globally consistent and end-bound. By proper choice of design parameters and initialized error variables, the tracking error can converge to an arbitrary small neighborhood of the origin and the L∞ tracking performance of the tracking error Be guaranteed. Numerical simulation shows the effectiveness of the method.