提出了一种基于自适应 Chebyshev 多项式神经网络(ACNN)的 Logistic 混沌系统控制算法。该算法采用 Chebyshev

正交多项式作为神经网络的激励函数, 构建 Logistic 混沌系统的预测与控制模型。为了保证算法的稳定性, 提出和证明了收敛定

理, 并利用自适应学习率算法提高神经网络的学习效率和收敛速度。通过采用自适应 Chebyshev 神经网络直接学习 Logistic 混

沌系统的动态特性, 并对系统实施目标函数控制。实验仿真结果表明, 该算法在 Logistic 混沌系统有外部干扰的情况下仍能对其

进行有效控制, 网络学习时间为 0.178 s, 训练步长为 10, 均方误差达到 1.15×10

− 4 , 与其他常见算法相比具有计算量小、速度快、

精度高和网络结构简单等优点。 - A novel algorithm for controlling Logistic chaotic system based on adaptive Chebyshev polynomials

neural networks (ACNN) is presented. In the algorithm, the activation function of hidden units is defined by Chebyshev

orthogonal polynomials in the neural networks, and the forecast and control model of Logistic chaotic system is estab-

lished. In order to ensure stability of the algorithm, the convergence theorem of the algorithm is proposed and proved.

Then　the　adaptive　learning　rate　algorithm　is　used　for　improving　the　learning　efficiency　and　convergence　speed.　The

adaptive Chebyshev neural networks directly learn dynamic characters of Logistic chaotic system and control it to target

function. The simulation results show that the algorithm is still effective when there are external disturbance in the Lo-

gistic chaotic system, now the learning time is 0.178s, training steps is 10 and mean square error is 1.15×10 − 4 . Com-

pared　with　other　ordinary