High-frequency nonlinear vibrational control

This paper discusses the feasibility of high-frequency nonlinear vibrational control. Such control has the advantage that it does not require state measurement and processing capabilities that are required in conventional feedback control. Bellman et al. (1986) investigated nonlinear systems controlled by linear vibrational controllers and proved that vibrational control is not feasible if the Jacobian matrix has a positive trace. This paper extends previous work to include nonlinear vibrational controllers. A stability criteria is derived for nonlinear systems with nonlinear controllers, and it is shown that a nonlinear vibrational controller can stabilize a system even if the Jacobian matrix has a positive trace.