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

'Indirect adaptive control for a class of non-linear systems with a time-varying structure', International This article maybe used for research, teaching and private study purposes. Any substantial or systematic reproduction, redistribution , reselling , loan or sub-licensing, systematic supply or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The accuracy of any instructions, formulae and drug doses should be independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims, proceedings, demand or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material. 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 ® nite 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.