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

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. As such, the well-established discrete-time adaptive control schemes can be easily applied to various control problems with periodic parameters, such as plants with unknown control directions, plants in parametric-strict-feedback form, plants that are nonlinear in parameters, plants that do not meet the linear growth condition, 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 several simulation examples.