Controller design for extending periodic dynamics of a chaotic CO2 laser

The paper considers a single-mode CO₂ laser that exhibits a cascade of period doubling bifurcations leading to chaos when it is driven by a sinusoidal signal of increasing amplitude. The requirement of a proper working of the laser, for relatively large amplitude of the forcing signal, naturally leads to the control problem of stabilizing periodic motions. Two control schemes are designed: the first one is based on delayed control signals for stabilizing unstable periodic orbits embedded in the chaotic attractor, while the second one relies on the cancellation of subharmonic components of the chaotic motions. Simulations and experimental tests are presented to show the control performance.