Page 229 - Adaptive Identification and Control of Uncertain Systems with Nonsmooth Dynamics

CHAPTER 15

Adaptive Neural Dynamic Surface

Control for Pure-Feedback

Systems With Input Saturation

15.1 INTRODUCTION

Among different non-linear systems, pure-feedback systems can cover more
realistic plants, while the control design for such systems is much more
challenging due to its non-affine property [1]. Classical control design of
pure-feedback system is to transform it into a strict-feedback form and then
tailor backstepping technique [2,3]. The well known issue in conventional
backstepping methods, the ‘complexity explosion’ problem caused by the
repetitive differentiation operation of virtual controls in each step, was fur-
ther remedied by introducing a first-order filter in each recursive design
step; this led to the subsequent dynamic surface control (DSC), e.g., [1,4].
However, the effect of input saturation is not considered in the aforemen-
tioned works.
To address the input saturation non-linearities imposed on the actua-
tors, some adaptive control schemes have been recently reported for various
non-linear systems [5–8]. In [6,9], adaptive neural controllers have been ob-
tained for controlling saturated non-linear systems with the bounds of input
saturation being known. Some recent work has been also presented without
knowing the bound of saturation dynamics. In [10], a smooth non-affine
function of the control input signal is used to approximate the non-smooth
saturation function, and a Nussbaum function is introduced to compensate
for the non-linear gain arising from the input saturation. Moreover, con-
sidering the function approximation abilities, neural networks (NNs) have
been used in the control designs to cope with the residual saturation errors
and other unknown system dynamics [11,12].
In this chapter, a neural dynamic surface control is developed for a class
of uncertain non-linear pure-feedback systems with unknown input satu-
ration. First of all, the non-linear pure-feedback system is transformed into
a canonical form by using the first-order Taylor expansion and coordinate
transformation. Moreover, to deal with the non-smooth input saturation
non-linearity, a smooth non-affine function is used to approximate the in-
Adaptive Identification and Control of Uncertain Systems with Non-smooth Dynamics.
DOI: https://doi.org/10.1016/B978-0-12-813683-6.00019-2 229
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