期刊
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
卷 461, 期 2063, 页码 3365-3380出版社
ROYAL SOC
DOI: 10.1098/rspa.2005.1516
关键词
piecewise smooth systems; grazing trajectories; grazing bifurcations; discontinuity mappings; control
A method is presented for controlling the persistence of a local attractor near a grazing periodic trajectory in a piecewise smooth dynamical system in the presence of discontinuous jumps in the state associated with intersections with system discontiunities. In particular, it is shown that a discrete, linear feedback strategy may be employed to retain the existence of an attractor near the grazing trajectory, such that the deviation of the attractor from the grazing trajectory goes to zero as the system parameters approach those corresponding to grazing contact. The implementation relies on a local analysis of the near-grazing dynamics using the concept of discontinuity mappings. Numerical results are presented for a linear and a nonlinear oscillator.
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