Page 180 - Adaptive Identification and Control of Uncertain Systems with Nonsmooth Dynamics

CHAPTER 11

Adaptive Dynamic Surface Output

Feedback Control of

Pure-Feedback Systems With

Non-linear Dead-Zone

11.1 INTRODUCTION

Pure-feedback systems can represent more generic practical plants, such as
aircraft systems, chemical processes, servomechanisms, and so on. How-
ever, the non-affine property of pure-feedback systems makes the feedback
control design difficult. In fact, the backstepping that has been originally
proposed for strict-feedback systems can not be directly used for pure-
feedback systems. Over the past decades, a notable idea is to represent a
pure-feedback system as a strict-feedback form by applying the mean value
theorem on the non-affine functions [1,2]. Following this idea, the implicit
function theorem was employed to assert the desired feedback controller
in [1]. This idea was also extended to non-affine pure-feedback systems [3],
where the ISS-modular approach and small gain theorem were employed.
Most of these control designs have been derived based on the assumption
that all system states are available or measurable.
On the other hand, to cope with unknown system dynamics, as stated
in the previous chapters, the function approximators (e.g., neural networks
and fuzzy logic systems) have also been used in adaptive control for some
specific pure-feedback systems, e.g., [4], [5]. Apart from these function
approximation based control, extended state observer (ESO) has been re-
cently developed [6,7]. In the ESO design, the system states and external
disturbances can be estimated simultaneously by considering all the lumped
uncertainties as an extended state, which is distinguished from the conven-
tional observer designs. Due to its satisfactory estimation performance, ESO
has been successively used in many realistic engineering applications. How-
ever, ESO based control cannot be directly used for pure-feedback systems
due to the non-affine property. To address this issue, in a recent work [8],
a new coordinate transformation was suggested for strict-feedback systems
to transform the unknown non-affine input function to a partially affine
Adaptive Identification and Control of Uncertain Systems with Non-smooth Dynamics.
DOI: https://doi.org/10.1016/B978-0-12-813683-6.00014-3 177
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