Nonlinear Dynamics and Ergodic Theory Methods in Control

Abstract

The public reporting burden for this .collection of information is estimated to average 1 hour per response, inclu:^ gathering and maintaining the data needed, and completing and reviewing the collection of information. SPONSOR/MONITOR'S ACRONYM(S) SPONSOR/MONITOR'S REPORT NUMBER(S) DISTRIBUTION/AVAILABILITY STATEMENTApproved for public release, distribution unlimited. SUPPLEMENTARY NOTES ABSTRACTWe have continued to work on control of complex nonlinear systems and pursued applications to control of mixing, control of nanoscale processes and control of microscale mixing. At the Pi's group, 1 graduate student (Umesh Vaidya) was working on the problem of control of discrete-time, conservative systems and quantum control. Another student (Zoran Levnajic) worked on problems in visualization of dynamical systems. A postdoctoral student (Dmitri Vainchtein) continued working on the problem of flow control using tools fi-om dynamical systems theory and vortex dynamics and pursued a problem in control of nanopartical seperation. The PI worked on ergodic theory methods for control of systems with drift and qptimazation of mixing in a paper appeared in the journal Nature. The PI also worked extending the framework for model validation of Random Dynamical Systems i the framework of the Koopman operator developed into dynamical systems treatment of uncertainty analysis.