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This study employs \(L^{\infty }\) optimal control to alter the dynamic response of a Duffing nonlinear oscillator. Melnikov’s method is utilized to identify the critical homoclinic bifurcation, with \(L^{\infty }\) control being responsible for its adjustment. Through the cross-entropy method, we determine the optimal control to minimize a specific objective function. Numerical simulations demonstrate that \(L^{\infty }\) control can effectively expand regions where homoclinic transversal intersections are avoided.

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Control of Homoclinic Bifurcation in a 2D Dynamical System Using the \(L^{\infty }\) Optimal Feedback Control

  • 会议论文

  • 发表日期：

    2025年

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  • Vinicius Piccirillo

摘要

This study employs \(L^{\infty }\) optimal control to alter the dynamic response of a Duffing nonlinear oscillator. Melnikov’s method is utilized to identify the critical homoclinic bifurcation, with \(L^{\infty }\) control being responsible for its adjustment. Through the cross-entropy method, we determine the optimal control to minimize a specific objective function. Numerical simulations demonstrate that \(L^{\infty }\) control can effectively expand regions where homoclinic transversal intersections are avoided.