Page 159 - Adaptive Identification and Control of Uncertain Systems with Nonsmooth Dynamics

CHAPTER 10

Adaptive Prescribed Performance

Control of Strict-Feedback

Systems With Non-linear

Dead-Zone

10.1 INTRODUCTION

As presented in the previous chapters, dead-zone is one of commonly en-
countered actuator non-linearities in practical systems, e.g., hydraulic servo
valves, electronic motors, which can be descried by a non-smooth func-
tion characterizing no output for a range of control inputs [1]. To address
the control design for systems with unknown dead-zone dynamics, several
techniques have been presented in the past decades, e.g., [1–10] and among
others. Apart from the classical inverse dead-zone model control designs
(suitable for linear dead-zone dynamics), recent research focuses on inverse
model independent adaptive control designs. The previous chapters have
introduced a recently reported idea to reformulate non-linear dead-zone as
a time-varying system. Chapter 9 also develops a dynamic surface control
(DSC) design for strict-feedback systems with time-delays and dead-zone
input, which remedies the “explosion of complexity” in the backstepping
designs. In fact, there have been many adaptive control schemes of uncer-
tain non-linear time-delay systems (see [11–19] and references therein).
However, in standard adaptive control designs with function approxima-
tion, e.g., neural networks (NNs) and fuzzy logic systems (FLSs), the online
learning process may be sluggish before it achieves convergence. This slug-
gish online learning process may lead to poor transient control response
(e.g., overshoot, convergence rate, and even steady-state error). In particu-
lar, for non-linear systems with both dead-zone input and time-delays, our
work presented in the previous chapter and [20] can guarantee the uniform
ultimate boundedness of the closed-loop system. However, the transient
performance of this DSC control (e.g., overshoot, undershoot, and con-
vergence rate) can not be strictly guaranteed and prescribed. Moreover, the
above mentioned adaptive control designs all assume that the input gain
Adaptive Identification and Control of Uncertain Systems with Non-smooth Dynamics.
DOI: https://doi.org/10.1016/B978-0-12-813683-6.00013-1 155
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