Computation and Control II pp 225-236 | Cite as

# Applications of Homogeneity to Nonlinear Adaptive Control

Chapter

## Abstract

This article is intended to bring together ideas from the geometric theory of nonlinear control systems, in particular the employment of homogeneity properties for asymptotic feedback stabilization, with a classical approach to adaptive control, in particular the regulation problem in the presence of unknown parameters. The control systems under consideration are of the form
The control u takes vaLues in R, x E R“ and the vectorfields f and g are explicitly linearly parametrized by the supposedly unknown parameter p E R, i.e.
where k and gi are smooth vectorfields on R“, and we suppose that f

$$\dot x\left( t \right) = f\left( {x\left( t \right),p} \right) + u\left( t \right)g\left( {x\left( t \right),p} \right)$$

(1.1)

$$f\left( {x,p} \right) = {f_0}\left( x \right) + p{f_1}\left( x \right)andg\left( {x,p} \right) = {g_0}\left( x \right) + p{g_1}\left( x \right)$$

(1.2)

_{°}(0) _ f1(0) = O. (Note, that this notion of linear parametrization is very much coordinate dependent.)### Keywords

Manifold Assure Stein Dinates A363## Preview

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© Springer Science+Business Media New York 1991