CONTROL LYAPUNOV FUNCTIONS FOR ADAPTIVE NONLINEAR STABILIZATION

For the problem of stabilization of nonlinear systems linear in unknow n constant parameters, we introduce the concept of an adaptive control Lyapunov function (aclf) and use Sontag's constructive proof of Artst ein's theorem to design an adaptive controller. In this framework the problem of adaptive stabilization of a nonlinear system is reduced to the problem of nonadaptive stabilization of a modified system. To illu strate the construction of aclf's we give an adaptive backstepping lem ma which recovers our earlier design.