Rigatos G, Wira P, Melkikh A
1Unit of Industrial Automation, Industrial Systems Institute, 26504 Rion, Patras, Greece.
Laboratoire MIPS, Université d' Haute Alsace, 68093 Mulhouse, France.
Cogn Neurodyn. 2019 Feb;13(1):89-103. doi: 10.1007/s11571-018-9510-4. Epub 2018 Oct 15.
The article proposes a nonlinear optimal control method for synchronization of neurons that exhibit nonlinear dynamics and are subject to time-delays. The model of the Hindmarsh-Rose (HR) neurons is used as a case study. The dynamic model of the coupled HR neurons undergoes approximate linearization around a temporary operating point which is recomputed at each iteration of the control method. The linearization procedure relies on Taylor series expansion of the model and on computation of the associated Jacobian matrices. For the approximately linearized model of the coupled HR neurons an H-infinity controller is designed. For the selection of the controller's feedback gain an algebraic Riccati equation is repetitively solved at each time-step of the control algorithm. The stability properties of the control loop are proven through Lyapunov analysis. First, it is shown that the H-infinity tracking performance criterion is satisfied. Moreover, it is proven that the control loop is globally asymptotically stable.
本文提出了一种用于具有非线性动力学且存在时延的神经元同步的非线性最优控制方法。以Hindmarsh-Rose（HR）神经元模型为例进行研究。耦合HR神经元的动态模型在一个临时工作点附近进行近似线性化，该临时工作点在控制方法的每次迭代时重新计算。线性化过程依赖于模型的泰勒级数展开以及相关雅可比矩阵的计算。对于耦合HR神经元的近似线性化模型，设计了一个H无穷控制器。对于控制器反馈增益的选择，在控制算法的每个时间步重复求解代数黎卡提方程。通过李雅普诺夫分析证明了控制回路的稳定性。首先，证明了满足H无穷跟踪性能准则。此外，还证明了控制回路是全局渐近稳定的。
