一种改进的非线性MIMO系统鲁棒自适应反推控制

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。

Improved Robust and Adaptive Backstepping Control for Nonlinear MIMO Systems

A novel robust control law design scheme based on Radial Based Function Neural Network (RBF NN) and backstepping control was proposed for a class of strict feedback nonlinear systems with uncertain nonlinear system functions and unknown external disturbance.Uncertain nonlinear system functions were approximated by employing RBF NN.The problem of explosion of terms in traditional backstepping design,which was caused by repeated differentiations of certain nonlinear functions such as virtual control,was eliminated by introducing the first order filter.Then,a robust item was introduced to compensate for both the approximation error and external disturbance,which could improve the robustness and guarantee much higher tracking accuracy.All signals in the close loop were guaranteed to be semi globally，uniformly andultimately bounded.The output tracking error was proved to converge to a small neighborhood around zero and the performance of system tracking error can be guaranteed by appropriately choosing design parameters and introducing an initializing technique.Simulation results demonstrate the effectiveness of the proposed method.