本文针对回声状态网络储层结构设计和关键参数选取的难题，提出了行为空间和补偿回声网络结构分别解决了网络参数难以选择及高阶非线性复杂模型预测精度低的问题，最后对低浓度瓦斯浓度发电过程控制中的浓度配比预测环节进行应用。本文主要研究内容如下：

首先，针对回声状态网络参数难以选择的问题，提出一种基于行为空间优化回声状态网络参数的方法。其实质是通过泛化等级、核心等级、记忆容量构建回声状态网络行为空间。优化算法采用新颖搜索遗传算法(NSGA)，该算法结合 K 近邻个体距离和NMSE，通过建立行为空间最低配置筛选基因来限定遗传算法的遗传方向，提高优化效率，进而找到影响网络性能的因素。该方法克服了传统回声状态网络(ESN)参数选择困难、遗传算法优化时间长且无合适理论阐明储层性能对任务的影响等缺陷，提升了优化效率和网络学习性能。通过NARMA-10和Laser实验表明，在合理迭代的情况下，本文所提NSGA方法优化ESN参数，学习性能优于增长回声状态网络1%-20%，且可以通过行为空间解释影响 ESN 网络性能的原因。

其次，针对传统回声状态网络难以有效应对高阶非线性复杂模型问题，在理论分析的基础上提出了一种双储层结构的误差补偿回声状态网络结构，并设计了该网络的学习算法。该网络由计算层和补偿层构成，计算层主要承担拟合任务，补偿层则作为状态跟随器，实时补偿由于计算层对期望方差估计不足而导致的幅值偏差。对多阶振荡器数据集的实验结果表明，本文所提网络结构较常规网络具有更高的稳定性和泛化性能，尤其对高阶非线性复杂模型的预测精度大幅度提升。

最后，针对传统PID在时变系统中控制稳定性与精确性不足的问题，在蓄热氧化装置的气体调配原理的基础上，推导了掺混浓度计算公式，并提出了一种在线回声状态网络超低浓度瓦斯配比模型。实验结果表明，较传统PID模型，RLS-ESN在对时变抽采瓦斯浓度掺混控制中能够动态调整参数，所以无论在稳定性还是控制效率均得到明显提升。

To solve the problems of reservoir structure design and essential parameter selection of echo state network, we proposed behaviour space and compensation echo state network to solve the issues of network parameters selection and low prediction accuracy of a complementary high-order nonlinear complex model, respectively. Finally, the concentration ratio prediction in the low-concentration gas power generation process is applied. The main research contents of this paper are as follows:

Firstly, aiming at the problem that it is challenging to select the parameters of an echo state network(ESN), optimizing the parameters of an echo state network based on behaviour space is proposed. In essence, ESN behaviour space is constructed by generalization level, core level and memory capacity. The optimization algorithm adopts a novel search genetic algorithm (NSGA), which combines the k-nearest neighbour individual distance and NMSE to set up the minimum configuration screening gene in the behaviour space to limit the genetic direction of the genetic algorithm, improve the optimization efficiency, and then find the factors that affect the network performance. This method overcomes the disadvantages of traditional ESN parameter selection difficulty. Genetic algorithm optimization time is long. There is no unified theory to explain the effect of reservoir performance on the task and improves the optimization efficiency and network learning performance. The experimental results show that the proposed NSGA method is close to the optimal ESN structure, and its learning performance is better than that of the growing echo state network. Behaviour space can explain the reasons affecting ESN performance through the behaviour space.

Secondly, aiming at the problem that the traditional echo state network is challenging to deal with the high-order nonlinear complex model effectively, this section proposes an echo state network with an error compensation structure of dual reservoir structure based on theoretical analysis and designs the learning algorithm of the network. The network consists of a computing layer and a compensation layer. The computing layer mainly undertakes the fitting task. The compensation layer acts as a state follower to compensate for the amplitude deviation caused by the computing layer's insufficient estimation of the expected variance in real-time. Experiments on multi-order oscillator data sets show that the proposed network structure has higher stability and generalization performance than conventional networks. The prediction accuracy of high-order nonlinear complex models is greatly improved.

Finally, aiming at the problem of insufficient control stability and accuracy of traditional PID in the time-varying system, based on the principle of gas allocation in regenerative oxidation device, the formula of mixing concentration is derived, and an online echo state network ultra-low concentration gas ratio model is proposed. The experimental results show that compared with the traditional PID model, RLS-ESN can dynamically adjust the parameters in the mixing control of time-varying gas extraction concentration, so both the stability and the control efficiency are significantly improved.