基于ELM的一类不确定性纯反馈非线性系统的Backstepping自适应控制

针对一类不确定性纯反馈非线性动力学系统，在中值定理、Backstepping控制的基础上，提出一种基于极限学习机（ELM）的自适应神经控制方法。ELM随机确定单隐层前馈网络（SLFNs）的隐含层参数，仅需调整网络的输出权值，能以极快的学习速度获得良好的推广性。在每一步的Backstepping设计中，应用ELM网络对子系统的未知非线性项进行在线逼近，通过Lyapunov稳定性分析设计的权值参数自适应调节律，可以保证闭环非线性系统所有信号半全局最终一致有界，系统的输出收敛于期望轨迹的很小邻域内。将所设计的控制方法应用于化工过程中的连续搅拌反应釜（CSTR）非线性系统实例中，仿真结果表明了控制方法的有效性。

Adaptive control for a class of uncertain pure-feedback nonlinear systems using Backstepping based on extreme learning machine

For a class of uncertain pure-feedback nonlinear dynamical systems, an adaptive neural control method using the extreme learning machine (ELM) is presented on the basis of mean value theorem and Backstepping control. As a kind of single-hidden layer feed forward networks (SLFNs), ELM, which randomly chooses hidden node parameters and analytically determines the output weights, shows good generalized performance at extremely fast learning speed. In the process of each step for the Backstepping controller design, the ELM network is used to approximate unknown nonlinear part of the subsystem. Meanwhile, the adaptive adjustment law of weights parameter by Lyapunov stability analysis is derived so that the semiglobal uniform ultimate boundedness of all signals in the closed-loop nonlinear system can be guaranteed and the output of the system can also converge to a small neighborhood of the desired trajectory. The employed control method is then applied to the instance of continuous stirred tank reactor (CSTR) system in the chemical process and the simulation results are presented to verify the effectiveness of the method.