一类非等阶分数阶非线性系统的神经网络控制

讨论一类不确定非线性分数阶非等阶（noncommensurate）的系统的控制问题。假设系统含的不确定包括正实不确定（positive real uncertainty）项和非线性函数完全未知，首先利用RBF神经网络近似未知非线性函数，再基于系统的连续频率分布模型将分数阶系统转化为等价的无穷维分布状态变量的整数阶系统，结合间接Lyapunov方法及线性矩阵不等式（LMI）方法，给出了系统鲁棒渐近稳定的充分条件。理论和实例仿真验证了方法的有效性。

Robust neural network control for a class of noncommensurate nonlinear fractional-order system

The paper is concerned with the problem of the robust control for a class of fractional order noncommensurate nonlinear systems with positive real uncertainty and nonlinear functions unknown. Firstly, the unknown functions have been approximated using RBF neural networks, and by introducing a continuous frequency distributed model the fractional order system is an equivalent integral-order system with infinite dimension, then using indirect Lyapunov approach and Linear Matrix Inequality （LMI） techniques, the sufficient condition for robust asymptotic stability of the closed loop system is presented. The validity of the proposed methods is demonstrated by numerical example.