Abstract
The dynamic extended delayed feedback control (DEDFC) is developed to stabilize multi-rotation unstable periodic orbits (UPOs). The multi-rotation UPO here refers to the UPO that rotates more than once in a period. The DEDFC is derived by applying a dynamic control technique on the standard extended delayed feedback control (EDFC), to improve its control performance. The DEDFC is designed to meet two objectives, including enlarging the stability region of the controlled UPOs and minimizing the magnitude of the greatest Floquet multiplier. Then, a multi-objective optimization problem (MOP) is formulated for the control design and is solved with the genetic algorithm and cell mapping hybrid method. Case studies indicate that the control effect of DEDFC significantly outperforms that of standard EDFC when the control parameters are appropriately designed. The DEDFC can stabilize some multi-rotation UPOs in a large stability region. However, the standard EDFC can keep those multi-rotation UPOs stable only in a small stability region or cannot stabilize them at all.
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