Abstract
Recent interest in the area of adaptive control has concentrated on the stability and robustness issues. Strong results have been obtained using Lyapunov and small gain type stability criteria. The purpose of this paper is to attack the robustness and stability issues from a different point of view. Namely from the point of view of nonlinear analysis. It is shown that a simple model reference adaptive control systems undergoes a Hopf or period doubling bifurcation and a number of period doublings before it goes chaotic and eventually unstable. This region is quite wide and it is conjectured that robust (local) stability may follow if the transition through the first bifurcation point can be avoided.
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