ℒ1 adaptive output feedback controller for minimum phase systems

This paper presents an £₁ adaptive output feed back controller for a class of uncertain nonlinear systems in the presence of time and output dependent unknown nonlinearities. As compared to earlier introduced £₁ adaptive output feedback control architectures, the architecture in this paper relies on system inversion, and is therefore limited to minimum phase systems. Similar to prior solutions in £₁ adaptive control theory, the feedback structure is comprised of the three main elements, involving predictor, adaptation laws and low-pass filter, with the only difference that the predictor here is an input predictor and not a state predictor. Whereas in prior architectures of £₁ adaptive output feedback control the verification of the sufficient condition for stability, written in terms of £₁ norm of cascaded systems, was not straightforward, the solution proposed in this paper, under mild assumptions on system dynamics, provides a complete parametrization of the low-pass filters for the design purposes. The closed-loop system achieves arbitrarily close tracking of the input and the output signals of the reference system. Simulations verify the theoretical findings.