Bifurcation effects in robust adaptive control

A specific adaptive control problem is analyzed in a search for the implication of undermodeling on the performance of adaptive control. The observed bifurcation phenomena (Hopf bifurcation, homoclinic points, etc.) indicate what kind of dynamical responses are possible in the adaptive system. Because these phenomena are structurally stable with respect to small (non)linear disturbances and singular perturbations, the results have significant implications for the generic adaptive control problem. Design principles are enunciated based on the bifurcation analysis. In particular, for the problem examined, it becomes apparent that a tradeoff between controller objective, adaptation speed, and robustness to plant specification is required