On adaptive stabilization of nonlinearly parameterized discrete-time systems

Most of the existing results on adaptive control of discrete-time systems are concerned with the case where the unknown parameters enter into the system in a linear way. For systems with nonlinearly parameterized unknown parameters, one problem in constructing the controller lies in the fact that the traditional least squares and gradient estimation based adaptive controller will have essential difficulties both numerically and analytically. This paper will study the adaptive stabilization of a basic class of nonlinearly parameterized systems, and will show that the system is globally adaptively stabilizable, provided that the sensitivity function of the unknown parameter has a linear growth rate. One implications of this result is that arbitrarily growing nonlinearities in the uncertainty model may be allowed for global adaptive stabilization.