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

We present a direct adaptive control method for a class of uncertain nonlinear systems with a time-varying structure. We view the nonlinear systems as composed of a finite number of “pieces,” which are interpolated by functions that depend on a possibly exogenous scheduling variable. We assume that each piece is in strict-feedback form, and show that the method yields stability of all signals in the closed-loop, as well as convergence 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 systems considered is a generalization of the class of strict-feedback systems traditionally considered in the backstepping literature. We also provide design guidelines based on L₂ bounds on the transient