我已将标题页附在此处。它是双面模板，但我拥有的是单面模板。.cls 包含以下代码。我如何将其设为双面？第二件事是我如何在完整页面上获取底部页脚“2405-8963 ......”。
这里是一个用于查看 .cls 文件的 overleaf 链接，因为我无法将其附加到这里。
答案1
问题代码使用了一个article.cls类（在工作目录中）这不是标准的文章类别。
为了避免混淆，使用了来自 IFAC LaTeX 风格
该文件ifacconf.cls已保存在工作目录中。
请求的两侧通过 making @twoside= true来设置
copyright在第一页使用的页面样式中添加了特殊页脚。
\documentclass{ifacconf} % ifacconf.cls in the working directory
\usepackage{graphicx}
\usepackage{natbib}
\usepackage{amsmath,amsfonts,amssymb}
\usepackage{mathrsfs}
\usepackage{upgreek,type1cm}
\usepackage{pgf}
\usepackage{helvet}
\usepackage{courier}
\usepackage{multirow,float}
%%*****************************************************
\makeatletter
\@twosidetrue % two side <<<<<<<<<<<<<<<<<<
\def\ps@copyright{\let\@mkboth\@gobbletwo
\footskip=20pt%
\def\@oddhead{}
\let\@evenhead\@oddhead
\def\@oddfoot{\parbox{\textwidth}{2405-8963 {\footnotesize\raisebox{0.3ex}{\textcopyright}}\ 2020, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. \\ Peer review under responsibility of International Federation of Automatic Control.}} % add footer inthe first page <<<<<<<<<<<<<<<
\let\@evenfoot\@oddfoot
}
\makeatletter
\pagestyle{headings}
%%*****************************************************
\usepackage{kantlipsum} % dummy text
\begin{document}
\begin{frontmatter}
\title{Stabilization of Flexible Spacecraft with Probabilistic Faults via Reliable Memory Sampled-data Control} \thanks{This work was supported by Council of Scientifc and Industrial Research (CSIR), India under EMR Project, F.No: 25(0273)/17/ EMRII dated 27-04-2017.}
\author[First]{B. Visakamoorthi},
\author[Second]{K. Subramanian},
\author[Third]{P. Muthukumar},
\address[First]{Department of Mathematics, The Gandhigram Rural Institute (Deemed to be University), Gandhigram-624302, Tamil Nadu, India. (e-mail:[email protected]).}
\address[Second]{The School of IT Information and Control Engineering, Kunsan National University, 558, Daehak-ro, Gunsan-si, Jeollabuk-do, 54150, Korea. (e-mail:[email protected]).}
\address[Third]{Department of Mathematics, The Gandhigram Rural Institute (Deemed to be University), Gandhigram-624302, Tamil Nadu, India. (e-mail:[email protected]).}
\begin{abstract}
Abstract: This paper investigates the problem of stability analysis for a flexible spacecraft model via the reliable memory sampled-data control technique. Unlike the previous studies, the actuator fault under the stochastic environment and signal transmission delay are considered to tackle the stabilization problem of flexible spacecraft model. In this regard, the random variable is introduced to characterize the probabilistic actuator fault, which satisfies the Bernoulli distribution. The delay-dependent looped Lyapunov-Krasovskii functional (LKF) is constructed with full information about the whole sampling interval to derive the stability and stabilization analysis of the proposed results. Thus, the designed memory sampled-data control for the given spacecraft model guarantees the asymptotic stability performance in the formation of linear matrix inequalities (LMIs). The numerical section illustrates the effectiveness of the proposed theoretical results.\\
\textcopyright\ 2020, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.
\end{abstract}
\begin{keyword}
Flexible spacecraft, Memory sampled-data control, Lyapunov-Krasovskii functional, Probabilistic faults.
\end{keyword}
\end{frontmatter}
\section{Introduction}
\vspace{-.2cm}
The flexible spacecraft model has paid considerable attention in diverse areas, such as communication, monitoring, navigation, resources observation, and so on (Wang et al. (2015), Di Gennaro. (2003)). From the requirements of future space missions, the high precision and stability attitude control for flexible spacecraft has become a most valuable topic. In this model with multiple damped modes, stability performance is a challenging issue. For example, Singh et al. (2004) have been designed the feedback adaptive control for spacecraft together with flexible appendages.
Until now, different control techniques have been proposed to analyze the flexible spacecraft model (for more details, see, Liu et al. (2019), Wu et al. (2016), Liu et al. $(2017))$. Among these control techniques, sampled-data control has attracted much attention due to the development of digital technology and communication (Sun et al. (2017)). For a sampled-data control, it only needs the information on the state of the system at the sampling instants to the controller during a specific sampling interval, which can reduce the amount of transmitted data and effectively save the communication bandwidth. Meanwhile, the sampling interval plays an essential role in sampleddata control design systems. For example, Lam et al. (2007) have considered the periodic sampling intervals for stabilization of chaotic systems, and this strategy limits the scope of applications. In this regard, the authors have focused on the design of sampled-data control with aperiodic sampling intervals for various dynamical systems (see, Zeng et al. (2019), Hua et al. (2015)). Besides, the memory sampled-data controller, when updating the signal successfully from the sampler to the controller and zero-order hold $(\mathrm{ZOH})$ at the time instant $t_{k}$ has experienced a constant signal transmission delay, which has been investigated widely in recent years (Liu et al. $(2017))$.
On the other hand, actuator plays an essential activity in control systems if it undergoes inevitable failures, which can cause the system poor performances or even instability. In addition, the challenging operating conditions of spacecraft systems can increase the existence of failures in actuator and controllers (Yin et al. $(2016))$. Also, the failure components of spacecraft cannot be fixed with replacement parts when the spacecraft is launched, and it may cause environmental and safety problems. Hence, these situations pose a massive challenge for attitude control systems (Shen et al. (2018)). To overcome this situation, the fault-tolerant control methods have been established for flexible spacecraft model which guarantee the effective and timely response to maintain the stability, and reliability of the spacecraft model with the components failure (Xiao et al. (2011), Ye et al. (2006)). For instance, Sakthivel et al. (2015) have been studied the spacecraft model of sampled data fault-tolerant control design without memory.
Notice that, most of aforesaid actuator failure scheme of flexible spacecraft have been established for the deterministic case. In fact, the actuator fault may be stochastic because of system component aging or damages. Recently, the problem of T-S fuzzy based flexible spacecraft model under stochastic actuator fault has been addressed by Sun et al. (2017). However, space environmental disturbances will affect the stability of the spacecraft. In particular, the performance of attitude control may be degraded by the elastic vibration of the flexible appendages (Liu et al. $(2012))$. Thus, it is essential to design the control scheme with robustness. This will overcome the various disturbances from the environment and structural vibrations of the flexible appendages. Also, the level of $H_{\infty}$ performance is an essential study to overcome the issues of the disturbances in the dynamical system. To mention a few, Wu et al. (2016) have been investigated the robust $H_{\infty}$ control problem for flexible spacecraft model. Zhang et al. (2014) studied the spacecraft model with fixed and partial failure values of the actuator fault matrix. Moreover, from the author's knowledge, the problem of reliable stabilization of flexible spacecraft systems with probabilistic actuator faults via memory-based sampled-data controller design is not yet discussed in the existing literature. Based on the above motivation, the main aspects and novelties for this paper compiled as follows:
\begin{itemize}
\item Distinct from some existing literature (Sakthivel et al. (2015), Zhang et al. $(2014))$, the actuator fault under the stochastic environment in the flexible spacecraft model is investigated.
\item When compared to the traditional sampled-data control scheme, a general realistic sampled-data control with constant signal transmission delay is considered.
\item In the construction of LKF, the full looped information about the sampling interval, from $x(t)$ to $x\left(t_{k}\right)$ and from $x(t)$ to $x\left(t_{k+1}\right)$ is involved.
\item The improved version of free-matrix-based integral inequality is utilized to solve the derivative of the looped LKF.
\item Comparing with Zhang et al. $(2014)$, the proposed control technique is not only overcome the issues of disturbances from structural vibrations of the flexible appendages but also able to tolerate the actuator failure with $H_{\infty}$ performance level.
\item Finally, the effectiveness of our obtained theoretical results is illustrated with the numerical simulation.
\end{itemize}
\kant[1-18] % added <<<<<<<<<<<<<<<
\end{document}