Controlling chaos of a dynamical system with discontinuous vector field

✍ Scribed by Haiyan Hu

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 379 KB
• Volume: 106
• Category: Article
• ISSN: 0167-2789
• DOI: 10.1016/s0167-2789(97)00023-7

✦ Synopsis

The paper presents how to control the chaos of dynamical systems with discontinuous vector field through the paradigm of a harmonically forced oscillator having a set-up elastic stop. It is first shown that the Poincar6 mapping of this oscillator is not smooth near the fixed point corresponding to a periodic motion that grazes the stop. Thus, the current control strategies based on the smooth mapping cannot be directly used to stabilize the chaotic motion near a periodic grazing motion. Then proposed is a piecewise-linear control strategy based on the piecewise-linearized Poincar6 mapping reconstructed from sampled data and on the pole assignment in two regions near the fixed point. The efficacy of the strategy is finally demonstrated via numerical simulations.