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### Adaptive神经模糊滑模容错控制方法在不确定非线性系统中的应用 #### 研究背景与意义本文提出了一种针对具有执行器效能故障和输入饱和特性的不确定非线性系统的自适应神经模糊滑模容错控制方法。随着模糊逻辑、神经网络等智能控制技术的发展，这些技术在复杂的非线性系统中得到了广泛应用。特别是对于那些定义不明确、模型不确定的系统，采用模糊控制方法可以有效提升控制性能。自适应模糊控制技术已被广泛应用于处理不确定非线性系统的控制问题。 #### 控制方案概述本文提出的控制方法主要由以下几个部分组成： 1. **参数依赖性去除**：通过在线更新策略，消除了控制系统设计中对执行器故障边界参数的依赖。这种在线更新机制使得控制系统能够适应实际系统的变化，从而提高其鲁棒性和适应性。 2. **神经模糊模型**：开发了一个神经模糊模型来逼近非线性系统中的不确定性项。神经模糊模型结合了神经网络的学习能力和模糊系统的规则表示能力，能够在没有先验知识的情况下逼近复杂系统的动态特性。 3. **滑模控制器设计**：设计了一个滑模在线更新控制器来估计执行器的故障边界。滑模控制是一种有效的控制策略，能够在系统存在不确定性时确保系统的稳定性。本文中的滑模控制策略还考虑了执行器故障和饱和的影响。 4. **系统稳定性验证**：利用李雅普诺夫方法验证了在执行器故障和饱和存在的条件下，系统能够达到渐近稳定状态。这种方法为证明控制策略的有效性和稳定性提供了理论依据。 #### 主要贡献本文的主要贡献包括： - 提出了一种新的自适应神经模糊滑模控制方法，该方法能够处理具有执行器故障和输入饱和的不确定非线性系统。 - 在线更新机制使得控制系统能够适应执行器故障边界的未知变化，提高了控制系统的鲁棒性和适应性。 - 通过神经模糊模型逼近非线性不确定性项，无需事先了解系统的具体结构和参数。 - 通过滑模控制策略估计执行器故障边界，即使在执行器失效或输入受限的情况下也能保持系统的稳定运行。 - 利用李雅普诺夫稳定性理论证明了在存在执行器故障和饱和的情况下系统的渐近稳定性。 #### 扩展应用文中还讨论了如何将所提出的自适应神经模糊控制方法扩展到其他类型的不确定非线性系统，包括具有积分滑模流形和其他流行的滑模面的系统。这种扩展增加了控制方法的应用范围，并进一步展示了其灵活性和通用性。 #### 数值仿真验证为了验证所提方法的有效性，文中给出了一个数值例子。通过仿真结果表明，在执行器故障和输入饱和存在的条件下，该方法能够有效地控制非线性系统并保持其稳定运行。这些结果为实际工程应用提供了有力的支持。本文提出了一种新颖且有效的自适应神经模糊滑模容错控制方法，该方法能够处理具有执行器故障和输入饱和特性的不确定非线性系统。通过理论分析和数值仿真实验，证明了该方法的有效性和实用性。这一成果对于解决复杂非线性系统中的控制问题具有重要意义，并为未来的控制理论和技术发展奠定了坚实的基础。

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2268 IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS: SYSTEMS, VOL. 47, NO. 8, AUGUST 2017

Adaptive Neural-Fuzzy Sliding-Mode Fault-Tolerant

Control for Uncertain Nonlinear Systems

Shiping Wen, Michael Z. Q. Chen, Senior Member, IEEE, Zhigang Zeng, Senior Member, IEEE,

Tingwen Huang, Senior Member, IEEE, and Chaojie Li

Abstract—This paper proposes an adaptive neural-fuzzy

sliding-mode control method for uncertain nonlinear systems

with actuator effectiveness faults and input saturation. The

parameter dependence of the control scheme is removed from

the bound of actuator faults by updating online. A neural-fuzzy

model is developed to approximate the uncertain nonlinear

terms and a sliding-mode online-updating controller is developed

to estimate the bound of the actuator with no prior knowl-

edge of the fault. The asymptotic stability is veriﬁed via the

Lyapunov method in the presence of actuator faults and satu-

ration. Furthermore, the adaptive neural-fuzzy control method

is extended to the uncertain faulty nonlinear systems with inte-

gral sliding-mode manifold as well as other popular sliding-mode

surfaces. A numerical example is presented to demonstrate the

effectiveness of the derived results.

Index Terms—Actuator fault, actuator saturation, neural-fuzzy

approximator, sliding-mode control (SMC), uncertain nonlinear

system.

I. INTRODUCTION

LONG with fuzzy logic and neural networks, intelligent

control systems have been developed rapidly over the

past few decades. Fuzzy-control methods have been utilized in

the complex ill-deﬁned nonlinear systems with effective tech-

niques. Adaptive fuzzy control method was applied for uncer-

tain nonlinear systems [3]–[14], [33], [34]. In general, there

Manuscript received June 2, 2016; revised September 2, 2016 and

November 16, 2016; accepted January 1, 2017. Date of publication

February 22, 2017; date of current version July 17, 2017. This work was

supported in part by the Natural Science Foundation of China under Grant

61403152, Grant 61402218, Grant 61673187, and Grant 61673188, in part by

the Research Grants Council of Hong Kong through General Research Fund

under Grant 106140120, and in part by the NPRP Grant NPRP 8-274-2-107

from the Qatar National Research Fund (a member of Qatar Foundation). The

statements made herein are solely the responsibility of the authors. This paper

was recommended by Associate Editor C.-C. Tsai. (Corresponding author:

Zhigang Zeng.)

S. Wen is with the School of Automation, Huazhong University of Science

and Technology, Wuhan 430074, China, the College of Science, Engineering

and Technology, Hamad bin Khalifa University, 23874, Doha, Qatar, and

also with the Key Laboratory of Image Processing and Intelligent Control

of Education Ministry of China, Wuhan 430074, China.

M. Z. Q. Chen is with the Department of Mechanical Engineering,

University of Hong Kong, Hong Kong (e-mail: mzqchen@hku.hk).

Z. Zeng is with the School of Automation, Huazhong University of Science

and Technology, Wuhan 430074, China, and also with the Key Laboratory of

Image Processing and Intelligent Control of Education Ministry of China,

Wuhan 430074, China (e-mail: zgzeng527@126.com).

T. Huang is with Texas A&M University at Qatar, Doha 23874, Qatar

(e-mail: tingwen.huang@qatar.tamu.edu.cn).

C. Li is with the Platform Technologies Research Institute, RMIT

University, Melbourne, VIC 3001, Australia (e-mail: chaojie.li@rmit.edu.au).

Color versions of one or more of the ﬁgures in this paper are available

online at http://ieeexplore.ieee.org.

Digital Object Identiﬁer 10.1109/TSMC.2017.2648826

are two main components in the developed controllers: ﬁrst,

a fuzzy system is employed to achieve feedback cancellation;

second, to make sure the augmented system stable on the basis

of the Lyapunov method, a robust compensator such as back-

stepping control [15], sliding-mode control (SMC) [16], [17],

∞

control [18], determines the tuning parameters in the fuzzy

system. These methods make systems stable in robust con-

trol schemes. However, some speciﬁc constrained conditions

are imposed for uncertain nonlinear systems such as known

boundness of the approximation errors. To overcome the difﬁ-

culties such as external disturbances and approximation errors,

some hybrid control techniques have been developed with var-

ious control components [19]–[21]. Although these methods

achieve favorable performances, the number of fuzzy rules

increases dramatically when the nonlinear system demon-

strates more degrees of freedom, which increases the difﬁculty

to implement the real-time control. In recent, neural-fuzzy net-

works have emerged with the learning capability of neural

networks and being widely adopted in the adaptive control to

deal with uncertainties in order to achieve desired performance

criteria [22]–[32].

With the advantages of high robustness to external distur-

bances [33]–[38], SMC has been utilized in many applica-

tions [39]–[46]. An ideal sliding mode can be achieved by

driving the augmented system to satisfy certain equation gov-

erning the sliding mode for all time. On the other hand, the

nonlinear uncertain systems are generally controlled with high

gains by the SMC method, which can easily lead to a chat-

tering phenomenon, therefore, some interest has been paid to

combine a sliding mode controller with fuzzy logic control

for nonlinear systems [47]. Thus, neural-fuzzy control is com-

bined with the SMC to ensure global stability and robustness

to disturbances,

However, uncertainties and nonlinearities are considered in

the case of no actuator fault or failure during the entire con-

trol process in most of the previous research, which is hardly

existed in practice [48]–[50]. In this way, the whole con-

trol objective will be failed ultimately with an abrupt fault

occurrence if no fault tolerance capability has been considered

for the designed controller. Thus, the control design should

address the issue of fault tolerance capacity [51]–[55]. As

another critical issue, actuator saturation should be tackled

in nonlinear control as well as fault tolerant control [51].

Since the output of the augmented actuators will be satu-

rated or constrained sometimes, which will destabilize the

augmented systems. In consequence, a lot of controllers

2168-2216

 2017 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.

See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

WEN et al.: ADAPTIVE NEURAL-FUZZY SLIDING-MODE FAULT-TOLERANT CONTROL FOR UNCERTAIN NONLINEAR SYSTEMS 2269

have been developed to effectively tackle the limited actua-

tor output [56]–[62]. However, actuator faults have not been

considered in these controllers. Therefore, these methods

cannot be directly applied to uncertain nonlinear faulty

systems.

Along with the increasing demands for reliability, fault tol-

erant control has drawn great attention in many ﬁelds such

as spacecrafts, motors, and robots. However, due to the non-

linearities and dynamics complexity, neural-fuzzy SMC for

uncertain nonlinear system with actuator faults and saturation

has not been investigated. Motivated by the above discus-

sion, this paper proposes a novel adaptive neural-fuzzy SMC

scheme for the uncertain nonlinear system with actuator fault

and saturation. Furthermore, the asymptotic stability is veriﬁed

based on the Lyapunov method in the presence of unmod-

eled dynamics, disturbance, actuator faults, and saturation. It is

worth pointing out that, the proposed control problem is non-

trivial because of the difﬁculties of: 1) neural-fuzzy approach

is utilized to approximate the unknown system dynamics;

2) online adaptive estimation of the bound of actuator fault

is exploited to achieve the control objective without any

mechanism of fault detection or isolation to determine the

information of actuator fault; 3) the control law is protected

from the actuator saturation with globally asymptotic stability;

and 4) the obtained adaptive control method can be extended

to augmented systems with some other popular sliding-mode

surfaces such as integral sliding manifold.

The rest of this paper is organized as follows. In Section II,

a dynamic model of uncertain faulty nonlinear system and

the problems to be investigated are formulated. In Section III,

description of the adaptive SMC subject to actuator fault is

presented. Sufﬁcient conditions of the asymptotic stability are

derived for the adaptive neural-fuzzy sliding-mode scheme

with actuator faults in Section IV. Fault tolerant controller

design is performed with actuator faults and saturation in

Section V. The obtained results are extended to the augmented

systems with the integral sliding mode surface in Section VI.

Simulation results are presented to demonstrate the effec-

tiveness of the obtained results in Section VII. Finally, the

conclusions are drawn in Section VIII.

II. P

ROBLEM DESCRIPTION

Consider the nth-order nonlinear dynamical system as

˙x

= f

(

)

+ g

(

)

αu + d

y = x

(1)

where

x =



x ˙x ··· x

(

n−1

)



[

··· x

]

∈ R

represents the vector of measurable states, u ∈ R and y ∈ R

denote the control input and system output, respectively, d

denotes the bounded external disturbance, f (x) and g(x) are

smooth uncertain nonlinear functions, g(x) is assumed to be

strictly positive, i.e., g(x) ≥ g

> 0, and α is the unexpected

actuator fault with 0 <α≤ 1. A solution is assumed for (1)

and the order of the nonlinear system (1) is known. The control

target is to design a control law for u to make the uncertain

nonlinear system (1) asymptotical stability with unexpected

actuator fault impactor α.

III. A

DAPTIVE SLIDING-MODE CONTROL

SUBJECT TO ACTUATOR FAULTS

In general, sliding mode control assumes that x is mea-

surable and f (x), g(x) are given. Many SMC methods have

been proposed. To make this paper easy to read, a sim-

ple linear sliding-mode surface is considered ﬁrst to derive

the main results which can be then extended to the popular

integral SMC.

Set a simple linear sliding-mode surface as

s =



i=1

, a

= 1(2)

where a

, i = 1,...,n− 1 are chosen such that



i=1

i−1

a Hurwitz polynominal. From (2), the following equation can

be derived as

=−

n−1



i=1

+ s. (3)

Let ˜x = [x

··· x

n−1

]

. Therefore, we can get the

reduce-order system of (1)

˜x =

A˜x +

[

00 ··· s

]

(4)

where

A =

⎡

⎢

⎣

010··· 0

001··· 0

−a

··· −a

n−1

⎤

⎥

⎦

Thus, if we constructed an appropriate controller u to satisfy

the sliding mode condition s˙s < 0, the states of system (1)

could asymptotically converge to zero.

Meanwhile, we can rewrite system (1)as

˙x

= f

(

)

(

)

+ g

(

))

αu + d (5)

where g

(x) is the nominal parameter of g(x), g(x) = g(x)−

(x) is the uncertain term.

Therefore, one has a corresponding equation

˙x

= f +

(

+ g

)

αu + d

= f + g

u +

(

αg

+ αg − g

)

u + d

= f + g

u + Mu + d (6)

with M = (α − 1)g

+ αg. Although g is time-varying and

uncertain, the following inequalities always exist:

−g

 g  g

−g  g  g

which are followed by

0.5 <

< 2

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