CONTROLLING HIGH-DIMENSIONAL UNSTABLE STEADY-STATES USING DELAY, DURATION AND FEEDBACK

We present a control method for stabilizing steady states using only d iscrete pulses of an available system parameter. In addition to the fe edback amplitude of the pulse, we employ the pulse width and delay as additional parameters. This allows us to stabilize steady states with more than one unstable direction and prevent unwanted transients in th e high-dimensional stable subspace. We have applied our method to a mo del of a multimode laser whose steady state becomes unstable due to a Hopf bifurcation and may exhibit periodic oscillations and chaos, We a lso show the importance of considering the delay between the system me asurement and application of control that will be present in any real experiment.