Stationary Bifurcation Control for Systems with Uncontrollable Linearization

摘要

Stationary bifurcation control is studied under the assumption that the critical zero eigenvalue is uncontrollable for the linearized system. The development facilitates explicit construction of feedback control laws that render the bifurcation supercritical. Thus, the bifurcated equilibria in the controlled system are guaranteed stable. Both pitchfork bifurcation and transcritical bifurcation are addressed. The results obtained for pitchfork bifurcations apply to general nonlinear models smooth in the state and the control. For transcritical bifurcations, the results require the system to be affine in the control.