Automatica 77 (2017) 103–111
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Automatica
journal homepage: www.elsevier.com/locate/automatica
Brief paper
Indirect neuroadaptive control of unknown MIMO systems tracking
uncertain target under sensor failures
✩
Yongduan Song
1
, Beibei Zhang, Kai Zhao
School of Automation, Chongqing University, Chongqing 400044, China
a r t i c l e i n f o
Article history:
Received 17 December 2015
Received in revised form
13 September 2016
Accepted 7 November 2016
Keywords:
Indirect neuroadaptive tracking control
Uncertain target
Sensor failures
Uniformly ultimately bounded (UUB)
Barrier Lyapunov Function (BLF)
a b s t r a c t
The problem of tracking a moving target with unknown trajectory is interesting and nontrivial. The
underlying problem becomes even more challenging if uncertain dynamics and sensor failures are
involved. This work presents an indirect adaptive neural network control strategy capable of making
uncertain multi-input multi-output nonlinear systems track a moving target with uncertain trajectory
closely despite sensor faults. An analytical model is proposed to allow the estimated (predicted) target
trajectory to be linked mathematically with the actual disguised (polluted) target trajectory, thus
facilitating the control design and stability analysis. A barrier Lyapunov function based design technique
is employed to ensure that the inputs to the neural network remain within the compact set such that
the neural network unit maintains its learning/approximating functionality during the entire process
of system operation. The proposed control scheme guarantees the boundedness of all the closed-loop
signals and the uniformly ultimately bounded stable tracking. Numerical simulation results also confirm
the effectiveness of the proposed neuroadaptive tracking control method.
© 2016 Elsevier Ltd. All rights reserved.
1. Introduction
Most practical control problems can be formulated as trajectory
tracking which includes both regulation and stabilization as two
special cases (i.e., regulation corresponds to the case that the
desired trajectory is constant, while stabilization corresponds to
the desired trajectory being strictly zero, respectively). For this
reason tracking control problem has been widely investigated
under various scenarios (Liu, Yu, & Zhong, 2014; Wang, Su, & Hong,
2004; Wu, Wu, Luo, & Guan, 2012; Zhou, Shi, Tian, & Wang, 2015)
and (Krstic, Kanelakopoulos, & Kokotovic, 1995; Li, Tong, & Li,
2015; Meng, Yang, Jagannathan, & Sun, 2014; Na, Ren, & Zheng,
2013; Wen & Ren, 2011). However, the vast majority of the existing
tracking control methods are based on the assumption that the
desired target trajectory is known a priori and the sensoring
✩
This work was supported in part by the Major State Basic Research Development
Program 973 (No. 2012CB215202, No. 2014CB249200) and the National Natural
Science Foundation of China (No. 61134001). The material in this paper was not
presented at any conference. This paper was recommended for publication in
revised form by Associate Editor Shuzhi Sam Ge under the direction of Editor
Miroslav Krstic.
E-mail addresses: ydsong@cqu.edu.cn (Y. Song), beibei@cqu.edu.cn (B. Zhang),
zhaokai@cqu.edu.cn (K. Zhao).
1
Fax: +86 023 65103001.
system works healthily during the entire system operation (Deng,
Li, & Wu, 2008; Dong, Zhao, Chen, & Farrell, 2012; Ge & Wang, 2004;
Ge & Zhang, 2003; Li, Tong, & Li, 2016; Sanner & Slotine, 1992;
Spooner & Passino, 1999; Zhang, Ge, & Hang, 2000).
It should be noted that, in many practical applications, the
desired trajectory to be tracked might not be available precisely.
For instance, in missile interception, the target to be intercepted
might be disguised on purpose or the target data might be
unconsciously damaged or unexpectedly polluted, rendering
the desired trajectory unavailable for guidance and control of
the interceptor (Alfriend, Vadali, Gurfil, How, & Breger, 2009).
Likewise, in industrial robotic applications (Akella, 2005; Loria,
Dasdemir, & Jarquin, 2016; Park & Han, 2011), for a given task the
desired trace for the end effector might not be available precisely
in advance, so that only the estimated trajectory can be used for
control design.
Another scenario causing imprecise trajectory information on
the target is that the target searching equipment for acquiring the
desired trajectory for the target is defected. Furthermore, sensoring
devices might malfunction during system operation. Therefore it
is of theoretical and practical importance to investigate tracking
control problem of nonlinear dynamic systems under unknown
desired target and sensor failures. To our best knowledge, very
little effort has been made in literature in addressing this
technically important issue (Bai, Arcak, & Wen, 2009; Wang,
Huang, Wen, & Fan, 2014; Yu & Xia, 2012).
http://dx.doi.org/10.1016/j.automatica.2016.11.034
0005-1098/© 2016 Elsevier Ltd. All rights reserved.