Control for a class of nonlinear systems with a time-varying structure

TLDR: In this paper, a direct adaptive control method for a class of uncertain nonlinear systems with a time-varying structure is presented, where each piece is in strict feedback form and 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.

Abstract: In this paper 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 here is a generalization of the class of strict feedback systems traditionally considered in the backstepping literature. We also provide design guidelines based on L-infinity bounds on the transient.