中文摘要：

神经网络模型经线性化后可构建神经预测控制框架,但是,对高阶项的忽略会产生大量未建模动态.本文以回声状态网络（Echo State Network,ESN）为代表,提出基于岭回归的未建模动态补偿方法.以线性化前后ESN内部状态观测的偏差作为表征未建模动态的样本,通过岭回归估计未建模动态与ESN状态变量之间的线性依存关系.将回归得到的补偿项内化为ESN储备池吸引子的平移和旋转,体现了吸引子的吸引力对激活函数边界约束作用的有效补充.两个实例验证了补偿方法对提高控制精度具有积极作用.

英文摘要：

Neural networks are often linearized to construct a framework of neural predictive control,but a challenging issue remains that lots of dynamics caused by omitting high-order terms are unmodeled. We took ESNs（ Echo State Networks） as a paradigm,and proposed a ridge regression method to compensate unmodeled dynamics. The unmodeled dynamics were observed by collecting the difference of ESN internal states before-and-after linearization,and they were represented by a linear function of ESN states estimated with ridge regressions. The compensation terms for the unmodeled dynamics were then internalized as movements and rotations of attractors in ESN reservoirs. The internalization provided a newpossibility ： The loss of boundary constraint because of linearization of activation functions can be partially remedied by the attraction effect of attractors. Two examples demonstrated that our compensation method could actively improve the control.