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Artif Life Robotics (2014) 19:347–353
DOI 10.1007/s10015-014-0173-x
ORIGINAL ARTICLE
An improved adaptive switching control based on quasi-ARX
neural network for nonlinear systems
Imam Sutrisno · Chi Che · Jinglu Hu
Received: 7 April 2014 / Accepted: 19 August 2014 / Published online: 15 October 2014
© ISAROB 2014
1 Introduction
Adaptive control of nonlinear dynamical systems has
attracted much attention and developed significantly dur-
ing the last of few decades. Many adaptive control methods
have been proposed and the corresponding stability and con-
vergence have been proved [1, 2]. Unfortunately, the perfor-
mance of linear control models cannot satisfy the require-
ment. Hence, some nonlinear prediction models have been
developed for nonlinear systems to overcome the difficulty
in design of predictor and controller for nonlinear systems.
One approach to identify and control nonlinear dynamical
systems is neural networks because of its ability to approxi-
mate the arbitrary mapping to any desired accuracy [3, 4, 5].
However, there are two major problems on those neu-
ral network models. The first, their parameters do not
have useful interpretations. The second, they do not have
a friendly interface for controller design and system analy-
sis. To solve these problems, in the previous work, a quasi-
linear auto regressive exogenous (quasi-ARX) neural net-
work (QARXNN) modeling scheme has been proposed
based on well-developed linear system theory and can be
extended to nonlinear systems. The models consist of two
parts: a macro model part and a kernel part [6, 7, 8]. The
QARXNN model has two properties: the linear property
and the nonlinear property. Based on the model character-
istics, two controllers can be obtained: one linear controller
and one nonlinear controller. The linear controller is used
to ensure the control stability and the nonlinear controller is
utilized to improve the control accuracy. The 0/1 switching
mechanism is proposed between the two controllers. If the
switching flag is 0, then a linear controller is employed oth-
erwise a nonlinear controller is employed. In such a way,
the quasi-ARX prediction model uses only one model to
achieve function of two or more models.
Abstract In this paper, an improved switching mecha-
nism based on quasi-linear auto regressive exogenous
(quasi-ARX) neural network (QARXNN) is presented for
the adaptive control of nonlinear systems. The proposed
switching control is composed of a QARXNN-based pre-
diction model and an improved switching mechanism using
two new adaptive control laws, first is moving average fil-
ter law and second is new switching law. Since the control
result of nonlinear predictor is better than the linear predic-
tor in most of the time, the adaptive control with a simple
switching mechanism has many useless switching during
the processing. Hence, the improved smooth switching
mechanism is proposed to replace the original switching
mechanism; it can improve the performance by reducing
the useless switching while guaranteeing stability of the
system control. The simulations show that the efficiency
of the proposed control method is satisfied in stability,
improve control accuracy and robustness.
Keywords Adaptive switching control · An improved
switching mechanism · Quasi-ARX neural network
prediction model
This work was presented in part at the 19th International
Symposium on Artificial Life and Robotics, Beppu, Oita, January
22–24, 2014.
I. Sutrisno · C. Che · J. Hu
Graduate School of Information, Production and Systems Waseda
University, Hibikino 2-7, Wakamatsu-ku, Kitakyushu 808-0135,
Fukuoka, Japan
I. Sutrisno (*)
Politeknik Perkapalan Negeri Surabaya, Jl. Teknik Kimia,
Kampus ITS Sukolilo, Surabaya 60111, Jawa Timur, Indonesia
e-mail: imams3jpg@moegi.waseda.jp