Boundedness properties of simple, indirect adaptive-control systems

Examining adaptive controllers for a class of first-order linear continuous-time plants, with different estimators, and control laws, the authors obtain explicit solutions completely describing the nonlinear behavior of the resultant adaptive systems. Some of these adaptive systems exhibit either finite time escapes, or other forms of unbounded behavior, due to a loss of stabilizability of the estimated model. Some fixes for the loss of stabilizability problem are analyzed. Implications of these results for the general indirect adaptive/control case are discussed.