Hopf Bifurcation Control of Nonlinear Oscillation Systems

This chapter addresses the problem of Hopf bifurcation amplitude control (HBAC), and applies it to the study of controlling the self-sustained oscillations in nonlinear systems. The sufficient conditions of the amplitude controllability of Hopf bifurcation are obtained for a specific kind of smooth affined control systems. The conditions show that curvature coefficient controllability implies oscillating amplitude controllability, and the HBAC problem can be solved by state feedback. Two examples demonstrate the correctness and effectiveness of Hopf bifurcation amplitude control.