07.05.2008. :: Predavanje Profesora G. Rega iz Italije
MATEMATICKI INSTITUT SANU, ODELjENjE ZA MEHANIKU
Sreda, 7. maj 2008.
Prof. Giuseppe Rega,
Dipartimento di Ingegneria Strutturale e Geotecnica,
Sapienza Università di Roma via A. Gramsci 53, 00197, Roma, Italy,
CONTROL OF BIFURCATION, CHAOS AND BASIN INTEGRITY: THEORETICAL ISSUES AND APPLICATION
Upon shortly addressing a systematic classification of methods for control of chaos and their applications to mechanical systems, a “universal” technique for controlling homoclinic or heteroclinic bifurcations of a hilltop saddle as the triggering event for the onset of transient, and possibly steady, chaos is presented. It is based on optimally choosing the shape of a periodic excitation applied to the considered system.
Features of dynamic integrity of nonlinear oscillators are analyzed, by critically reviewing the definition of safe basin of attraction, the formulation of suitable integrity measures, and the construction of basin erosion profiles with a varying control parameter.
Hints are given on the practical capability of the control method to regularize fractal basin boundaries, reduce their erosion, and delay the occurrence of chaos or escape for various mechanical systems.
The effectiveness of the method as regards controlling the dynamic pull-in phenomenon in the nonlinear dynamics of an electrically actuated thermo-elastic micro-beam is specifically addressed by referring to a relevant minimal reduced-order model. Extensive numerical simulations highlight the good performances of the method also beyond theoretical expectations.