An adaptive control system with a first-order plant and the so-called
sigma-modification adaptation law is analyzed in the case of periodic
disturbance or reference input. The local bifurcations of the low-peri
od solutions are numerically detected by means of a continuation metho
d, and the different modes of behavior are classified as well as the t
ransitions among them. As predicted by the theory, the control system
is robust in the sense that all trajectories are bounded regardless to
the action of the disturbance. However, the periodicity of the input
can give rise to chaotic behavior. The result of the analysis will aid
the designer in selecting the controller parameters in order to achie
ve an acceptable behavior.