Abstract:

Concerning the problem of identification of parameters and time delay for chaotic systems with unknown delay， a parameter identification model for time-delay chaotic systems based on temporal attention mechanism was proposed， namely Parameter Identification Neural Network with Temporal Attention （PINN-TA）. Firstly， the time delay identification was implemented by applying temporal attention mechanism to extract correlation features within system state sequences. Then， the algebraic equations of system parameters were formed by implicitly approximating system differential equation with the use of recurrent neural network. Finally， the roots of these equations were taken as the results of parameter identification. With typical time-delay chaotic systems including delay Logistic equation， Ikeda differential equation and Mackey-Glass chaotic system used as identificated objects， PINN-TA model was compared with multiple intelligent search algorithms in experiments. Simulation results show that PINN-TA model has the identification error of parameters and time delay 90.31% to 99.36% lower in comparison with existing intelligent search algorithms such as Artificial Raindrop Algorithm （ARA）， Hybrid Cuckoo Search （HCS）， Global Flower Pollination Algorithm （GFPA） and Cellular Whale Algorithm （CWA）， while the identification time of the proposed model is shortened to 18.59 to 19.43 ms. It can be seen that PINN-TA model can meet the accuracy and real-time requirements， and provides a feasible solution for identification of parameters and time delay for time-delay chaotic systems.

Key words: delay chaotic system, parameter identification, Recurrent Neural Network (RNN), temporal attention mechanism, state sequence

摘要：

针对时滞混沌系统在时滞未知条件下的参数及时滞辨识问题，提出基于时间注意力机制的时滞混沌系统参数辨识模型——PINN-TA。首先，采用时间注意力机制提取系统状态序列的关联特征，以实现对系统时滞的辨识；其次，利用循环神经网络（RNN）隐式地近似系统微分方程，形成关于系统参数的代数方程；最后，将代数方程的根作为参数辨识的结果。分别以时滞Logistic方程、Ikeda微分方程和Mackey-Glass混沌系统等典型时滞混沌系统作为待辨识系统，对PINN-TA模型和多种智能搜索算法进行对比实验。仿真结果表明，相较于人工雨滴算法（ARA）、混合布谷鸟搜索算法（HCS）、全局花朵授粉算法（GFPA）、元胞自动机鲸鱼算法（CWA）等现有智能搜索算法，PINN-TA模型对参数和时滞的辨识误差降低了90.31%~99.36%，且辨识耗时缩短至18.59~19.43 ms。可见，PINN-TA模型能够满足精度和实时性要求，为时滞混沌系统参数及时滞辨识提供可行的解决方案。

关键词: 时滞混沌系统, 参数辨识, 循环神经网络, 时间注意力机制, 状态序列