HIGH-FREQUENCY NONLINEAR VIBRATIONAL CONTROL

This paper discusses the feasibility of high-frequency nonlinear vibra tional control. Such control has the advantage that it does not requir e state measurement and processing capabilities that are required in c onventional feedback control. Bellman et al. [1] investigated nonlinea r systems controlled by linear vibrational controllers and proved that vibrational control is not feasible if the Jacobian matrix has a posi tive trace. This paper extends previous work to include nonlinear vibr ational controllers. A stability criteria is derived for nonlinear sys tems with nonlinear controllers, and it is shown that a nonlinear vibr ational controller can stabilize a system even if the Jacobian matrix has a positive trace.