饱和鲁棒自适应控制：新型近似模型在非线性系统中的应用

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"这篇研究论文探讨了不确定非线性系统在输入饱和情况下的自适应跟踪控制问题。通过构建一个新的近似饱和模型，该模型能够以任意预设精度平滑地近似实际饱和非线性，有效地处理了非光滑饱和非线性的影响。作者采用了动态表面控制方法，并结合改进的线性滤波器，明确设计了一种鲁棒自适应控制方案，通过添加积分技术来消除误差。提出的控制器能够在保证系统性能的同时，克服输入饱和和不确定性带来的挑战。" 在不确定非线性系统的研究中，控制策略的设计往往是一项复杂任务，特别是在存在输入饱和的情况下。输入饱和是指系统中控制器或执行器的能力有限，导致无法进一步增加或减少控制输入，这在实际工程应用中很常见。论文中提出的新方法是针对这一问题的一个解决方案。首先，为了处理饱和非线性，作者构建了一个新颖的近似饱和模型。这个模型不同于传统的离散逼近，它可以以任意精度平滑地近似实际的饱和特性，降低了非线性对控制系统稳定性的影响。这样的模型不仅简化了控制器设计，还有助于提高系统的动态性能。接着，论文引入了动态表面控制(Dynamic Surface Control, DSC)方法。DSC是一种将滑模控制与自适应控制相结合的技术，它通过动态表面来消除传统滑模控制中的抖动问题，同时保持良好的控制性能。在此基础上，作者结合了改进的线性滤波器，以进一步优化控制信号并减小噪声影响。为了实现精确的跟踪控制，控制方案中加入了积分器。积分器的引入可以消除稳态误差，确保系统在长期运行中能够准确跟踪设定值。同时，由于系统的不确定性，鲁棒控制策略必不可少。论文中的控制方案考虑了这些不确定性，设计出的控制器具有鲁棒性，能有效应对系统参数的变化和外部扰动。这篇论文为不确定非线性系统的饱和鲁棒自适应控制提供了一种创新方法，通过新的近似模型和优化的控制结构，解决了输入饱和问题，提高了系统稳定性和控制精度。这种方法对于实际工程应用具有重要的理论指导意义和实践价值。

IET Control Theory & Applications

Brief Paper

Saturated robust adaptive control for

uncertain non-linear systems using a new

approximate model

ISSN 1751-8644

Received on 5th August 2016

Revised 7th December 2016

Accepted on 25th December 2016

E-First on 14th February 2017

doi: 10.1049/iet-cta.2016.0979

www.ietdl.org

Yong-Hua Liu

Hunan Provincial Key Laboratory of Health Maintenance for Mechanical Equipment, Hunan University of Science and Technology, Xiangtan,

Hunan 411201, People's Republic of China

E-mail: yonghua.liu@outlook.com

Abstract: In this study, the authors consider the problem of adaptive tracking control for a class of non-linear uncertain systems

in the presence of input saturation. To tackle the effects of the non-smooth saturation non-linearity, a novel approximate

saturation model is constructed, which can smoothly approximate the real saturation with arbitrarily prescribed precision. By

utilising dynamic surface control approach with the modified linear filters, a robust adaptive control scheme is explicitly designed

via the adding an integrator technique. The proposed controller can eliminate not only the ‘explosion of complexity’ issue

inherent in the backstepping design but also the coupling terms with respect to the surface errors and the boundary layer errors.

In addition, the stability analysis shows that all the resulting closed-loop signals are semi-global uniformly ultimately bounded.

Finally, simulation results are presented to demonstrate the performance of the developed method.

1 Introduction

In many industrial processes, the magnitude of control signals is

usually constrained due to the limitation of the actuators or the

safety requirements. As one of the commonly non-smooth non-

linearities, saturation always limits system performance severely

by giving rise to undesirable inaccuracy or oscillations, and even

leads to instability [1, 2]. Driven by practical interests and

theoretical challenges, the development of adaptive control design

for compensating the effects of saturation non-linearity has become

a hot topic [3, 4]. Several efficient methods have been proposed for

linear and non-linear systems with input saturation, such as model

reference adaptive control [5, 6], model predictive control [7, 8],

anti-windup control [9, 10], low-gain control [11, 12], and

intelligent control [13–17]. Other remarkable approaches include

reference governors [18], variable structure control [19, 20], and

dynamic inversion control [21].

However, most of the available adaptive control schemes for

systems with input saturation are descriptive rather than

constructive. As a constructive tool, the use of backstepping

approach for considering saturation non-linearity has recently

attracted considerable attention. In [22], a novel on-line

approximation based backstepping control was proposed for non-

linear systems in the presence of known magnitude, rate, or

bandwidth constraints on the states or actuators. For a class of

uncertain multi-input–multi-output (MIMO) non-linear systems

with input constraints and unknown control coefficient matrices, a

robust backstepping-based neural network controller was presented

via variable structure control and Lyapunov synthesis [23]. In [24],

to mitigate the effects of input non-linearities in MIMO non-linear

systems, an auxiliary design system was introduced and its states

were used to develop adaptive tracking control. In [25], constrained

adaptive backstepping control was proposed for the F-16/MATV

(multi-axis thrust vectoring) aircraft. In [26], by exploring the non-

smooth properties of saturation non-linearity, a well defined

smooth function was employed to approximate the saturation with

a bounded approximation error, then two global robust adaptive

control schemes were proposed for uncertain non-linear systems

with input saturation and external disturbance. Inspired by the

method in [26], significant results were developed for unknown

non-linear systems with input saturation [27–31]. In [32], by

utilising the robust integral of the sign of the error methodology, a

continuous saturation control law with smooth saturation functions

was designed for a class of second-order, uncertain non-linear

time-varying systems with bounded disturbances. In [33], a dead-

zone operator-based model was proposed to describe saturation

non-linearity, and the corresponding robust adaptive controller was

developed for a class of non-linear saturated non-linear systems. In

[34], by utilising a novel sliding mode disturbance observer, robust

constrained control was presented for cascade non-linear MIMO

systems with input saturation and unknown external disturbance.

Although numerous results by using backstepping technique are

available for non-linear systems with input saturation in the

literature, a main barrier, called the ‘explosion of complexity’

problem, may limit the practical implementation of these control

schemes. To overcome this problem, a dynamic surface control

(DSC) approach, which was proposed originally in [35, 36], has

been studied extensively to deal with the effects of saturation non-

linearity. In [37], the problem of simultaneous quadratic

stabilisation for a class of non-linear systems with input saturation

was studied, a DSC scheme of estimating the ellipsoidal initial

condition set was proposed to ensure the quadratic stabilisation. In

[38–42], by using a hyperbolic tangent function (HTF) defined in

[26], adaptive approximation-based DSC schemes were presented

for various classes of non-linear systems with input saturation. In

[43], the authors addressed adaptive control for a class of MIMO

non-affine pure-feedback systems with input saturation and time

delays, an adaptive neural DSC approach was obtained by

integrating mean value theorem and the auxiliary system. To

handle the effects of input saturation and stochastic disturbance, an

adaptive DSC approach was proposed for a class of stochastic non-

linear systems using the existing dead zone-based model of

saturation [44]. For interconnected non-linear systems in the

presence of input saturation, a decentralised neural DSC method

was presented via a novel truncated adaptation design [45].

Motivated by the above-mentioned works, in this paper, the

problem of adaptive tracking for strict-feedback non-linear systems

in the presence of input saturation is investigated. Instead of using

the existing HTF proposed in [26], the saturation input non-

linearity is approximated by a new approximate saturation model,

which can smoothly approximate the real saturation with any

prescribed accuracy. By utilising the adding an integrator technique

and DSC approach, the design difficulties induced by the non-

affine fashion in augmented system and the problem of ‘explosion

of complexity’ inherent in the backstepping method are removed.

Based on the Lyapunov stability theory, it is proven that all signals

IET Control Theory Appl., 2017, Vol. 11 Iss. 6, pp. 870-876

870

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