Discrete-time adaptive control for nonlinear systems with periodic parameters: A lifting approach

Abstract

In this paper we develop a general discrete-time adaptive control approach suitable for nonlinear systems with periodic parametric uncertainties. The underlying idea of the new approach is to convert the periodic parameters into an augmented constant parametric vector by a lifting technique. The novelty of this approach is the establishment of a bridge between classical adaptive control problems and periodic adaptive control problems. As such, the well-established discrete-time adaptive control schemes can be easily applied to various control problems with periodic parameters, such as plants that do not meet the linear growth condition, plants that are nonlinear in parameters, plants with unknown control directions, plants in parametric-strict-feedback form, etc. Another major advantage of the new adaptive control is the ability to adaptively update all parameters in parallel, hence expedite the adaption speed. The effectiveness of the proposed approach is illustrated by simulation. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society.