Application of linear ordinary differential equations to the stability control of long time lag networks
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 stabili...
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| Published in: | Applied mathematics and nonlinear sciences Vol. 9; no. 1 |
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| Language: | English |
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01.01.2024
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| 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 (< 1.0
− 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
= 0.52,
= 0.71 and
= 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. |
|---|---|
| AbstractList | 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 (< 1.0
− 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
= 0.52,
= 0.71 and
= 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. 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 (< 1.0 e − 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, T 1 = 0.71 and T 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. 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. |
| Author | Yao, Haiyan |
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| Cites_doi | 10.1016/j.chaos.2021.111374 10.1109/TCYB.2018.2803754 10.1109/TSG.2015.2474815 10.1515/gmj-2016-0077 10.1109/TR.2021.3063492 10.1007/s11071-017-3905-3 10.1063/1.5111686 10.1016/j.csda.2022.107483 10.3390/en14185820 10.1109/TIE.2018.2870384 10.1016/j.neucom.2017.09.050 10.1103/PhysRevLett.122.058301 10.1007/s11139-015-9753-1 10.1016/j.sysconle.2017.07.012 10.1007/s11071-017-3455-8 10.1016/j.automatica.2019.03.017 10.1109/TPWRS.2020.3032471 10.3390/en14216899 10.1002/mma.6064 |
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| SubjectTerms | 78-02 Fixed-time synchronization Intermittent control Network control systems Ordinary differential equations Structural stability Systems stability Time-lag systems |
| Title | Application of linear ordinary differential equations to the stability control of long time lag networks |
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