<abstract xmlns="http://www.w3.org/1999/xhtml">

Optimal control based on the exact synchronization of linear ordinary differential equations can provide conditions for the existence of optimal control of long-time lag network stability. In this paper, we first generalize network control systems, time lag systems, and modern control system stability theory to discuss long-time lag network stability analysis and control problems. The numerical solution method for solving ordinary differential equations with boundary conditions is proposed by combining the numerical solution method for initial value problems of differential equations and the iterative method for solving nonlinear equations. Finally, the fixed-time synchronization problem of complex networks with time-varying time lags under periodic intermittent control is studied. Two intermittent control strategies are designed based on the linear ordinary differential equation algorithm, and the convergence analysis of the synchronization error and the synchronization criterion are given. Numerical values show that the synchronization error converges to zero (&lt; 1.0<italic>e</italic> − 5) in 0.32s, while the convergence times are 0.55s and 0.90s. The fixed times of the three methods are calculated to be <italic>T</italic>* = 0.52, <italic>T</italic>1 = 0.71 and <italic>T</italic>2 = 1.32, respectively, and the synchronization error system converges faster under the method in the paper. The numerical simulation results verify the effectiveness of linear ordinary differential equations in controlling the stability of long-time lag networks.
</abstract>

Optimal control based on the exact synchronization of linear ordinary differential equations can provide conditions for the existence of optimal control of long-time lag network stability. In this paper, we first generalize network control systems, time lag systems, and modern control system stability theory to discuss long-time lag network stability analysis and control problems. The numerical solution method for solving ordinary differential equations with boundary conditions is proposed by combining the numerical solution method for initial value problems of differential equations and the iterative method for solving nonlinear equations. Finally, the fixed-time synchronization problem of complex networks with time-varying time lags under periodic intermittent control is studied. Two intermittent control strategies are designed based on the linear ordinary differential equation algorithm, and the convergence analysis of the synchronization error and the synchronization criterion are given. Numerical values show that the synchronization error converges to zero (< 1.0e − 5) in 0.32s, while the convergence times are 0.55s and 0.90s. The fixed times of the three methods are calculated to be T* = 0.52, T1 = 0.71 and T2 = 1.32, respectively, and the synchronization error system converges faster under the method in the paper. The numerical simulation results verify the effectiveness of linear ordinary differential equations in controlling the stability of long-time lag networks.

Application of linear ordinary differential equations to the stability control of long time lag networks

Applied Mathematics and Nonlinear Sciences

This work is licensed under the Creative Commons Attribution 4.0 International License.

Optimal control based on the exact synchronization of linear ordinary differential equations can provide conditions for the existence of optimal control of...

Application of linear ordinary differential equations to the stability control of long time lag networks

Published Online: Oct 09, 2023

Page range: -

Received: Dec 31, 2022

Accepted: Apr 19, 2023

DOI: https://doi.org/10.2478/amns.2023.2.00572

Keywords
Ordinary differential equations, Network control systems, Time-lag systems, Structural stability, Fixed-time synchronization, Intermittent control

© 2023 Haiyan Yao, published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Application of linear ordinary differential equations to the stability control of long time lag networks

Published Online: Oct 09, 2023

Page range: -

Received: Dec 31, 2022

Accepted: Apr 19, 2023

DOI: https://doi.org/10.2478/amns.2023.2.00572

KeywordsOrdinary differential equations, Network control systems, Time-lag systems, Structural stability, Fixed-time synchronization, Intermittent control

© 2023 Haiyan Yao, published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Keywords
Ordinary differential equations, Network control systems, Time-lag systems, Structural stability, Fixed-time synchronization, Intermittent control