Abstract Since most real-world processes exhibit both nonlinear and time-varying characteristics, there exists a need for accurate and efficient models that can adapt in nonstationary environments. Also for adaptive control purpose, it is vital that an adaptive model has a fixed small model size. In this paper, we propose an adaptive tunable gradient radial basis function (GRBF) network for online modeling of nonlinear dynamic processes, which meets these practical requirements. Specifically, a compact GRBF model is constructed by the orthogonal least squares algorithm in training, which is capable of modeling variations of local mean and trend in the data well. During online operation, the adaptive GRBF model tacks the time-varying process’s dynamics by replacing a worst performing node with a new node which encodes the current new data. By exploiting the local predictor property of the GRBF node, the new node optimization can be done extremely efficiently. The proposed approach combining the advantages of both the GRBF network structure and fast tunable node mechanism is capable of tracking the time-varying nonlinear dynamics accurately and effectively. Extensive simulation results demonstrate that the proposed fast tunable GRBF network significantly outperforms the existing state-of-the-art methods, in terms of both adaptive modeling accuracy and online computational complexity.

中文翻译：

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用于非线性和非平稳动态过程在线建模的快速可调梯度 RBF 网络

摘要 由于大多数现实世界的过程都表现出非线性和时变特征，因此需要能够适应非平稳环境的准确有效的模型。同样出于自适应控制的目的，自适应模型具有固定的小模型尺寸至关重要。在本文中，我们提出了一种自适应可调梯度径向基函数（GRBF）网络，用于非线性动态过程的在线建模，满足这些实际要求。具体来说，在训练中通过正交最小二乘算法构建了一个紧凑的GRBF模型，能够很好地对数据中局部均值和趋势的变化进行建模。在在线操作期间，自适应 GRBF 模型通过用编码当前新数据的新节点替换性能最差的节点来跟踪时变过程的动态。通过利用 GRBF 节点的局部预测器特性，可以非常有效地完成新节点优化。所提出的方法结合了 GRBF 网络结构和快速可调节点机制的优点，能够准确有效地跟踪时变非线性动力学。广泛的仿真结果表明，所提出的快速可调 GRBF 网络在自适应建模精度和在线计算复杂度方面都明显优于现有的最先进方法。所提出的方法结合了 GRBF 网络结构和快速可调节点机制的优点，能够准确有效地跟踪时变非线性动力学。广泛的仿真结果表明，所提出的快速可调 GRBF 网络在自适应建模精度和在线计算复杂度方面都明显优于现有的最先进方法。所提出的方法结合了 GRBF 网络结构和快速可调节点机制的优点，能够准确有效地跟踪时变非线性动力学。广泛的仿真结果表明，所提出的快速可调 GRBF 网络在自适应建模精度和在线计算复杂度方面都明显优于现有的最先进方法。