Stability and Hopf Bifurcation of PD-Controlled XCP Network Congestion Model

Na Han; Yanhui Zhai

doi:https://doi.org/10.14445/22315373/IJMTT-V67I9P516

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 67 | Issue 9 | Year 2021 | Article Id. IJMTT-V67I9P516 | DOI : https://doi.org/10.14445/22315373/IJMTT-V67I9P516

Stability and Hopf Bifurcation of PD-Controlled XCP Network Congestion Model

Na Han, Yanhui Zhai

Citation :

Na Han, Yanhui Zhai, "Stability and Hopf Bifurcation of PD-Controlled XCP Network Congestion Model," International Journal of Mathematics Trends and Technology (IJMTT), vol. 67, no. 9, pp. 138-145, 2021. Crossref, https://doi.org/10.14445/22315373/IJMTT-V67I9P516

Abstract

Based on feedback control and bifurcation theory, a PD controller is proposed to solve the Hopf branch problem of XCP network congested power system. Firstly, α is selected as the branching parameter to obtain the critical value that keeps the original system and the controlled system stable. When the delay value passes the critical value, the system will lose stability at the equilibrium point and Hopf branch will be generated. Then, the addition of PD controller increases the critical value of system branch parameters, expands the stability region, and effectively alleviates the generation of Hopf branches. Finally, the feasibility of theoretical analysis is verified by numerical simulation with mathematical software.

Keywords

Hopf bifurcation, PD controller, Stability, network congestion

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