华中科技大学学报（自然科学版）2025，Vol.53Issue(6)：145-154,10.DOI:10.13245/j.hust.250620
单自由度分段线性系统共存吸引子的转迁控制及优化
Transfer control and optimization of coexisting attractors for single-degree-of-freedom segmented linear system
摘要
Abstract
Aiming at the phenomenon of attractor coexistence in a class of single-degree-of-freedom segmented linear systems,the velocity pulse method was utilized for the transient control of the coexisting attractors of the system,and the control gains of the control method were optimized based on the adaptive inertia-weighted particle swarm optimization(APSO)algorithm.First,the Poincaré mapping of the system was obtained by constructing a local mapping,and the eigenvalues of the Jacobi matrix were calculated,and then the Floquet multipliers and Lyapunov exponents of the system were obtained.The shooting method,the cell mapping method and the parametric continuation algorithm were used to analyze the attractor coexistence phenomenon of the periodic motion of the system during transitions,which was induced by saddle-node bifurcation,period-doubling bifurcation and boundary crisis.Secondly,based on the velocity pulse method,a disturbance was applied to the velocity of the controlled periodic motion in the fixed phase plane to control the periodic motion or chaotic of the controlled system to other periodic motions coexisting with it.Finally,the APSO algorithm was utilized to optimize the control gains,and the optimal combination of control gains in the feasible region was obtained,which avoided the one-sidedness and inaccuracy of the controller gains determined by the trial-and-error method.The control method is conducive to improving the stability of the mechanical system and increasing the service life,which has certain practical significance in engineering.关键词
碰撞振动/转迁特征/分岔/吸引子共存/粒子群优化算法Key words
vibro-impact/transition characteristics/bifurcation/attractor coexistence/particle swarm optimization algorithm分类
机械工程引用本文复制引用
丁旺才,李孟,李得洋,吴少培,李国芳..单自由度分段线性系统共存吸引子的转迁控制及优化[J].华中科技大学学报（自然科学版）,2025,53(6):145-154,10.基金项目
国家自然科学基金资助项目(12262017,12162020) （12262017,12162020）
甘肃省青年科技基金资助项目(21JR7RA328,23JRRA1697) （21JR7RA328,23JRRA1697）
中央引导地方科技发展资金资助项目(24ZYQA044). （24ZYQA044）
