• [2012-10-30]

  Flow Barriers and Switchability in Discontinuous Dynamical Systems

Speaker：Dr. Albert C.J. Luo   Host：Caishan Liu   Time：15:00 pm

Date：November 3, 2012

Venue：Conference Room 434, Mechanics Building   Abstract: 

The theory of flow barriers in discontinuous dynamical systems are  systematically presented for the first time, which help one re-think the existing theories of stability and control in dynamical systems.  The concept of flow barriers in discontinuous dynamical systems are introduced, and the passability of a flow to the boundary with flow barriers are presented. Because the flow barriers exist on the boundary, the switchability of a flow to such a separation boundary are changed accordingly. The coming and leaving flow barriers in passable flows are discussed first, and the necessary and sufficient conditions for a flow to pass through the boundary with flow barrier are developed. Flow barriers for sink and source flows are also discussed. Once the sink flow is formed, the boundary flow barriers in the sink flow needs to be considered, and such a flow barrier is independent of vector fields in the corresponding domains.  Furthermore, when the boundary flow in the sink flow disappears, the vector fields should satisfy the appropriate conditions. Thus, the necessary and sufficient conditions for formations and vanishing of a sink flow are presented for a discontinuous dynamical system possessing flow barriers on the boundary. A periodically forced friction model will be presented as an example for a better understanding of flow barrier existence in physical problems. The flow barrier theory presented in this chapter will provide a theoretic base for one to further develop control theory and stability.

Bio-Sketch: Dr. Albert C.J. Luo, ASME Fellow, has been working on the theory and application of Nonlinear Dynamics and Mechanics for more than 20 years. Dr. Luo developed the theory of global transversality in nonlinear dynamical systems. Dr. Luo<span courier="" new';="" mso-ascii-font-family:="" calibri"="" lang="EN-US">’s theory of stochastic and resonant layers in nonlinear Hamiltonian systems systematically described the resonance mechanism of chaos. The local theory of discontinuous dynamical systems developed by Dr. Luo is instrumental in solving many difficult problems in science and engineering, such as  gear transmission systems and control systems. Dr. Luo has found the  analytical solutions for perioidc flows and chaos in nonlinear dynamical systems. Dr. Luo has published over 200 peer-reviewed journal and conference papers, ten monographs and seven edited books on Nonlinear Dynamics and Nonlinear Mechanics. He has been an Editor for the journal Communications in Nonlinear Science and Numerical Simulation since 2002, and an Editor for book series on Nonlinear Systems and Complexity (Springer). He has been a member of editorial board for IMeCh E Part K Journal of Multi-body Dynamics since 2002 and Journal of Vibration and Control since 2005.