Control and stochastic dynamic behavior of Fractional Gaussian noise-excited time-delayed inverted pendulum system

• Published in: Communications in nonlinear science & numerical simulation 2024-12, Vol.139, p.108302, Article 108302
• Main Authors: Li, Tianxu, Sun, Xudong, Wang, Qiubao, Guo, Xiuying, Han, Zikun
• Format: Article
• Language: English
• Subjects: Control; Fractional Gaussian noise; Hopf bifurcation; Inverted pendulum system; Time delay
• ISSN: 1007-5704
• DOI: 10.1016/j.cnsns.2024.108302

In this paper, we investigate the control and dynamic behavior of the inverted pendulum system with time delay under fractional Gaussian noise excitation. For H=1/2 and H∈(1/2,1), we analyze the stochastic dynamic characteristics of the system under Hopf bifurcation, utilizing time delay and noise intensity as bifurcation parameters, and validate the theoretical conclusions through numerical simulations. We also defined the engineering application range of angle and angular velocity under both asymptotically stable and periodic oscillation dynamic states. Furthermore, using the stochastic Itoˆ equation, we determined the values of time delay and noise intensity that satisfy the maximum engineering application range of angle and angular velocity, and verified their accuracy against the original equation. Additionally, we observed stochastic D-bifurcation and P-bifurcation arising from the combined effects of time delay and noise. Our results exhibit remarkable consistency between analytical and numerical findings, affirming the robustness of our approach and shedding light on the intricate dynamics of the system. •We investigate systems with time delays under fractional Gaussian noise excitation, thus paving the way for a deeper exploration of nonlinear phenomena in stochastic delay differential equations.•In the case of H = 1/2 and H ∈ (1/2, 1), we use different stochastic average methods to derive the Itô stochastic differential equation of the system, and verify the effectiveness and accuracy of the reduction through numerical simulations, and give the maximum time delay and noise intensity values for the engineering application range satisfying the angular and angular velocity under the excitation of Gaussian noise and fractional-order Gaussian noise, respectively.•Under H=1/2 and H∈(1/2,1), we utilize numerical simulations to unveil the complex dynamics of the system under different conditions. Simultaneously, we provide theoretical support for the control range of angle and angular velocity in engineering applications from another perspective, complementing the control section of the inverted pendulum.