Indirect adaptive control for a class of non-linear systems with a time-varying structure

In this paper we present an indirect adaptive control method for a class of uncertain non-linear systems with a time-varying structure. We view the non-linear 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 indirect adaptive 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 constants. The class of systems considered here is a generalization of the class of strict feedback systems traditionally considered in the backstepping literature. Finally, we apply the indirect adaptive method to the problem of regulation of aircraft wing rock with a time-varying angle of attack.