IEEE Trans Cybern. 2015 Aug;45(8):1587-96. doi: 10.1109/TCYB.2014.2356414. Epub 2014 Sep 26.
In this paper, first, an adaptive neural network (NN) state-feedback controller for a class of nonlinear systems with mismatched uncertainties is proposed. By using a radial basis function NN (RBFNN), a bound of unknown nonlinear functions is approximated so that no information about the upper bound of mismatched uncertainties is required. Then, an observer-based adaptive controller based on RBFNN is designed to stabilize uncertain nonlinear systems with immeasurable states. The state-feedback and observer-based controllers are based on Lyapunov and strictly positive real-Lyapunov stability theory, respectively, and it is shown that the asymptotic convergence of the closed-loop system to zero is achieved while maintaining bounded states at the same time. The presented methods are more general than the previous approaches, handling systems with no restriction on the dimension of the system and the number of inputs. Simulation results confirm the effectiveness of the proposed methods in the stabilization of mismatched nonlinear systems.
在本文中，首先提出了一种用于一类具有不匹配不确定性的非线性系统的自适应神经网络（NN）状态反馈控制器。通过使用径向基函数神经网络（RBFNN），逼近未知非线性函数的界，因此不需要不匹配不确定性的上界信息。然后，设计了基于 RBFNN 的观测器自适应控制器，以稳定具有不可测状态的不确定非线性系统。状态反馈和基于观测器的控制器分别基于 Lyapunov 和严格正实 Lyapunov 稳定性理论，并且表明闭环系统的渐近收敛到零，同时保持状态的有界。所提出的方法比以前的方法更具一般性，处理系统不受系统维度和输入数量的限制。仿真结果证实了所提出的方法在不匹配非线性系统稳定化中的有效性。
