Adaptive control for a class of nonlinear systems with a time-varying structure

In this note, we present a direct adaptive control method for a class of un certain nonlinear systems with a time-varying structure. We view the nonlin ear systems as composed of a Finite number of "pieces," which are interpola ted by functions that depend on a possibly exogenous scheduling variable. W e assume that each piece is in strict-feedback form, and show that the meth od yields stability of all signals in the closed-loop, as well as convergen ce of the state vector to a residual set around the equilibrium, whose size can be set by the choice of several design parameters. The class of system s considered here is a generalization of the class of strict-feedback syste ms traditionally considered in the backstepping literature. We also provide design guidelines based on L-2 bounds on the transient.