一类不确定切换系统容错控制的平均停留时间方法及应用实例

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本文主要探讨了一类不确定切换线性时滞系统容错控制的平均停留时间方法。在当前的研究领域中，对于这类系统的控制策略设计，特别是在存在执行器故障的情况下，是一个重要的挑战。作者提出了一种创新的平均停留时间控制策略，旨在确保即使在面对执行器故障时，系统仍能保持稳定并实现有效控制。文章的核心贡献包括： 1. 平均停留时间独立性：与先前的研究相比，这个方法的一个显著特点是，只要切换过程在平均意义上足够缓慢，那么控制策略就不依赖于具体的切换策略选择。这意味着设计者可以选择最适合实际应用的切换规则，而不用担心其对控制效果的影响。 2. 故障容忍稳定性：作者证明了所提出的控制设计能够确保带有执行器故障的一类时滞线性系统的指数稳定性。这意味着，即使在部分执行器失效的情况下，系统也能保持稳定的性能，这对于工业控制系统的可靠性至关重要。 3. 通用处理方式：这种方法的一大优点是它的普适性。它不需要预先识别哪个执行器存在问题，所有执行器都以统一的方式进行处理，简化了故障检测和隔离的过程，提高了整体系统的效率。 4. 实际应用示例：为了验证理论的有效性，作者将这一方法首次应用于水污染控制系统。在这个实际场景中，它处理了不同比例的流入流速和流出流速，展示了方法在动态环境中的实用性，对于环保工程具有重要的实际意义。这篇研究论文不仅提供了一种新的控制技术，还展示了如何将其应用到具有挑战性的实际问题中，如水污染控制，这进一步突显了其在工业电子领域的潜在价值和影响力。

IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 66, NO. 4, APRIL 2019 3139

An Average Dwell-Time Method for

Fault-Tolerant Control of Switched Time-Delay

Systems and Its Application

Ying Jin , Youmin Zhang , Senior Member, IEEE, Yuanwei Jing, and Jun Fu , Senior Member, IEEE

Abstract—This paper presents an average dwell-time

method for fault-tolerant control of a class of uncertain

switched linear time-delay systems and also designs an

algorithm to determine the parameters pertaining to the

dwell-time condition. Compared to the literature results,

this paper features the following: 1) the proposed method

is independent of switching polices if switchings are slow

enough in the average sense; 2) the proposed control

design guarantees exponential stabilization of this class of

time-delay linear systems with actuator faults; and 3) this

method treats all actuators in a uniﬁed manner without a

need to identify which are faulty or healthy actuators. The

proposed method is applied to the water pollution control

problem, for the ﬁrst time, to deal with different ratios of

stream ﬂow rates to efﬂuent ﬂow rates.

Index Terms—Fault-tolerant control, switched systems,

uncertainties.

I. INTRODUCTION

IME delay can be seen in various practical applications

such as chemical processes, long-distance transmission

networks, and automotive control. When time delay is present

in a dynamic system, it may deteriorate transient performance or

even lead to instability. When time delay is present in a dynamic

system, it may deteriorate transient performance or even lead

to instability. As an important class of hybrid dynamic systems,

switched time-delay systems (i.e., switched systems involving

time delay) have gained much attention for the control issues

[3]–[6] (and see the references therein). Due to the hybrid nature

of switched systems and the complicated features of the time

Manuscript received December 13, 2017; revised April 19, 2018; ac-

cepted May 28, 2018. Date of publication June 28, 2018; date of current

version November 30, 2018. This work was supported in part by the Na-

tional Natural Science Foundation of China under Grant 61503065, Grant

61573282, Grant 61473063, and Grant 61773108, and in part by the

Fundamental Research Funds for the Central Universities under Grant

N170804004 and Grant N150802001. (Corresponding author: Jun Fu.)

Y. Jin and J. Fu are with the State Key Laboratory of Synthetical

Automation for Process Industries, Northeastern University, Shenyang

110819, China (e-mail: jymontreal@gmail.com; junfu@mail.neu.

edu.cn).

Y. Zhang is with the Department of Mechanical, Industrial and

Aerospace Engineering, Concordia University, Montreal, QC H3H 1G8,

Canada (e-mail: youmin.zhang@concordia.ca).

Y. Jing is with the Department of Information Science and Engi-

neering, Northeastern University, Shenyang 110819, China (e-mail:

ywjjing@mail.neu.edu.cn).

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/TIE.2018.2847684

delay [7]–[11], [38] to be explored, studies on switched time-

delay systems are still one of the most important research topics

in control areas. Studies on switched time-delay systems are still

one of the most important research topics in control areas.

Another issue in the highly automated industrial systems is

that maintenance or repairs cannot always be provided immedi-

ately to preserve reliability and safety of the industrial systems.

Thus, the presence of uncertain faults and the possibility of faults

occurrence have to be taken into account in the process of the

system stability analysis and controller design to avoid heavy

economic costs or life-threatening prices caused by faults, e.g.,

see the recent important results [1], [2], [12]–[15], [34], [35],

[39]–[41], [44], [45], which lead fault-tolerant control to obtain

more and more attention [16]–[20]. Panagi and Polycarpou [16]

developed a decentralized fault-tolerant controller for a class of

interconnected nonlinear systems, which include ﬁnite subsys-

tems to ensure desired tracking performance and stabilization of

the closed-loop systems. In [16], only bounded fault functions,

which satisfy the so-called matching conditions and bounded

uncertain structures of the interconnected systems have been

considered, it did not explicitly take care of the faulty actua-

tors that directly transmit controller signals into the considered

plant. Wang et al. [17]–[20] presented fault-tolerant controllers

for the nonlinear systems with actuator faults to guarantee re-

liable stability of the systems. Their common feature is that

actuators are decomposed into two parts, one of which is sus-

ceptible to faults, and the other of which is robust to faults, to

compensate for actuator faults effectively. However, in order to

implement the controller designs, the two-part decomposition

has to be known in advance. It is, in general, difﬁcult to obtain

in practice due to uncertain and random feature of faults.

However, there are few results reported on fault-tolerant con-

trol of switched systems and that of switched time-delay systems

[3]–[5], [17], [18], [21], [22]. Wang et al. [4], [17], [21] gave suf-

ﬁcient conditions under which the proposed robust fault-tolerant

controller can control the class of nonlinear switched systems

after decomposing actuators into two groups, in the same man-

ner as in [18], i.e., one group is robust to actuator faults, but the

other is susceptible to the faults. Thus, the proposed methods in

[4], [17], and [21] have the same disadvantages from the fault

modeling and characterization viewpoint. Additionally, s truc-

tural uncertainties of input matrices, which can destabilize the

systems, were not considered for this class of switched systems

in [4], [17], and [21]. I n [22], by combining the safe-parking

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