A remark on chaotic behavior in adaptive control systems

This note deals with the control of a linear discrete-time system designed on the assumptions that we do not have explicit knowledge of the order of the plant. The objective is to cause the output to track a given constant reference y*, when the initial conditions are in a neighborhood of y*. In previous papers the presence of chaos was conjectured for an adaptive scheme where the plant to be controlled was a second-order one undermodeled by a first-order one. We show that with an adequate choice of the parameter estimator local regulation with exponential convergence of both the output and the parameter is obtained