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摘要: 针对一类难以建立精确模型的单输入单输出(Single-input single-output, SISO) 非线性离散动态系统, 提出了一种数据驱动模型的自适应控制方法. 所提方法首先设计具有直链与增强结构的随机配置网络(Stochastic configuration network, SCN), 建立了一种可同时表征非线性系统低阶线性部分与高阶非线性项(未建模动态)的数据驱动模型, 并采用增量学习方法与监督机制, 对模型结构与模型参数进行同步更新优化, 保证了数据驱动模型的无限逼近能力, 解决了传统自适应控制采用交替辨识算法存在的建模精度低、模型收敛性无法保证的问题. 进而利用直链部分与增强部分, 分别设计了线性控制器及虚拟未建模动态补偿器, 建立了基于SCN 数据驱动模型的自适应控制新方法, 分析了其稳定性与收敛性, 通过数值仿真实验和采用交替辨识算法的传统自适应控制方法进行对比, 实验结果表明了所提方法的有效性.Abstract: For a class of single-input single-output (SISO) nonlinear discrete dynamical systems which are difficult to establish an accurate model, a novel adaptive control method is proposed based on data-driven model. In the proposed approach, stochastic configuration network (SCN) is first employed to build the data-driven nonlinear system model, which adopts direct link and enhancement nodes to approximate the low-order linear and the high-order nonlinear parts (unmodeled dynamics) of system, respectively. Besides, this paper employed an incremental learning algorithm and supervision mechanism to optimize the model structure and model parameters synchronously, which guarantee the universal approximation property of the data-driven model, solving the problems of low modeling accuracy and unguaranteed model convergence existing in traditional adaptive control with alternate identification algorithm. Then, the direct link and enhancement nodes are used to design the linear controller and virtual unmodeled dynamics compensator respectively. A new adaptive control approach based on SCN data-driven model is established, and the stability and convergence of the proposed control method are proved. Finally, simulation comparisons between our proposed method and the classic adaptive control method with alternate identification algorithm are made, showing the effectiveness of the proposed method.
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图 2 基于SCN数据驱动模型的自适应控制方法结构图
Fig. 2 Structure diagram of adaptive control method with SCN-based data-driven model
图 8 基于SCN数据模型的灰分含量跟踪控制输出
Fig. 8 Output of ash content tracking control based on SCN data-driven model
图 9 基于SCN数据模型的重介质选煤灰分含量估计误差曲线
Fig. 9 Estimation error curve of ash content in dense medium separation process based on SCN data model
表 1 模型性能对比
Table 1 Performance comparison of models
模型性能指标 增强节点个数 离线建模
时间 (s)模型在线平均
绝对误差传统RVFLNN模型 17 0.257 19 0.004 6 SCN模型 9 0.245 82 0.001 3 
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表 2 控制系统模型估计性能对比
Table 2 Comparison of performance of model estimates for control systems
基于不同模型的自适应控制系统 ${\rm MAE}$ 基于线性模型的自适应控制 0.009 2 基于BP交替辨识模型的自适应控制 0.007 0 基于ANFIS交替辨识模型的自适应控制 0.005 1 基于SCN数据模型的自适应控制 0.001 3
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