陈海涛 . 航天器姿态跟踪及姿态协同有限时间控制方法研究 [D ] . 哈尔滨 : 哈尔滨工业大学 , 2019 : 3 - 16 .

CHEN H T . Research on finite-time attitude tracking control and attitude coordination control methods for spacecraft [D ] . Harbin : Harbin Institute of Technology , 2019 : 3 - 16 . (in Chinese)

刘金龙 . 车载液压柔性机械臂的轨迹跟踪及振动抑制方法研究 [D ] . 长春 : 长春工业大学 , 2018 : 44 - 59 .

LIU J L . Research on trajectory tracking and vibration suppression of vehicle hydraulic flexible manipulator [D ] . Changchun : Changchun University of Technology , 2018 : 44 - 59 . (in Chinese)

陈维乐 , 都海波 . 一种基于齐次系统理论的二阶离散超螺旋控制算法 [J ] . 控制理论与应用 , 2022 , 39 ( 4 ): 761 - 769 .

CHEN W L , DU H B . A second-order discrete-time super-twisting control algorithm based on homogeneous system theory [J ] . Control Theory & Applications , 2022 , 39 ( 4 ): 761 - 769 . (in Chinese)

刘畅 , 杨锁昌 , 汪连栋 , 等 . 基于快速自适应超螺旋算法的制导律 [J ] . 北京航空航天大学学报 , 2019 , 45 ( 7 ): 1388 - 1397 .

LIU C , YANG S C , WANG L D , et al. Guidance law based on fast adaptive super-twisting algorithm [J ] . Journal of Beijing University of Aeronautics and Astronautics , 2019 , 45 ( 7 ) : 1388 - 1397 . (in Chinese)

杨芳 , 张宽桥 , 余磊 . 自适应非奇异快速终端二阶滑模制导律 [J ] . 弹道学报 , 2020 , 32 ( 2 ): 7 - 15 .

YANG F , ZHANG K Q , YU L . Adaptive nonsingular fast terminal second-order sliding mode guidance law [J ] . Journal of Ballistics , 2020 , 32 ( 2 ): 7 - 15 . (in Chinese)

文成馀 , 江驹 , 余朝军 , 等 . 高超声速飞行器超螺旋滑模自适应控制 [J ] . 电光与控制 , 2020 , 27 ( 2 ): 1 - 5 .

WEN C Y , JIANG J , YU C J , et al. Super-twisting sliding mode adaptive control of hypersonic vehicle [J ] . Electronics Optics & Control , 2020 , 27 ( 2 ): 1 - 5 . (in Chinese)

李军 , 廖宇新 , 李珺 , 等 . 三维多变量超螺旋固定时间滑模制导律 [J ] . 电光与控制 , 2020 , 27 ( 10 ): 47 - 52 , 61.

LI J , LIAO Y X , LI J , et al. Three-dimensional multivariable super-twisting fixed-time sliding mode guidance law [J ] . Electronics Optics & Control , 2020 , 27 ( 10 ): 47 - 52 , 61. (in Chinese)

冯振欣 , 郭建国 , 周军 . 高超声速飞行器新型预设性能控制器设计 [J ] . 宇航学报 , 2018 , 39 ( 6 ): 656 - 663 .

FENG Z X , GUO J G , ZHOU J , et al. Novel prescribed performance controller design for a hypersonic vehicle [J ] . Journal of Astronautics , 2018 , 39 ( 6 ): 656 - 663 . (in Chinese)

JEYASENTHIL R , CHOI S B . A new anti-windup compensator based on quantitative feedback theory for an uncertain linear system with input saturation [J ] . Applied Sciences , 2019 , 9 ( 15 ): 2958 . DOI: 10.3390/app9152958 http://doi.org/10.3390/app9152958 https://www.mdpi.com/2076-3417/9/15/2958 https://www.mdpi.com/2076-3417/9/15/2958 This paper devotes to the robust stability problem for an uncertain linear time invariant (LTI) feedback system with actuator saturation nonlinearity. Based on a three degree of freedom (DOF) non-interfering control structure, the robust stability is enforced with the describing function (DF) approach for an uncertain LTI system to avoid the limit cycle. A new type of anti-windup (AW) compensator is designed using the quantitative feedback theory (QFT) graphical method, which results in a simple design procedure and low-order AW control system. One of the most significant benefits of the proposed method is free of the non-convexity (intractable) drawback of the linear matrix inequality (LMI)-based approach. The analysis conducted on the benchmark problem clearly reveals that the proposed QFT-based anti-windup design is able to handle both saturation and uncertainty in a very effective manner.

QIN H D , LI C P , SUN Y C , et al. Adaptive trajectory tracking algorithm of unmanned surface vessel based on anti-windup compensator with full-state constraints [J ] . Ocean Engineering , 2020 , 200 : 106906 . DOI: 10.1016/j.oceaneng.2019.106906 http://doi.org/10.1016/j.oceaneng.2019.106906 https://linkinghub.elsevier.com/retrieve/pii/S0029801819309916 https://linkinghub.elsevier.com/retrieve/pii/S0029801819309916

吴跃飞 , 马大为 , 乐贵高 . 控制受限的火箭炮位置伺服系统鲁棒自适应反步控制 [J ] . 兵工学报 , 2013 , 34 ( 4 ): 477 - 483 . DOI: 10. 3969/ j. issn. 1000-1093. 2013. 04. 015 http://doi.org/10. 3969/ j. issn. 1000-1093. 2013. 04. 015 针对火箭炮位置伺服系统运行过程中所存在的转动惯量和负载力矩变化大,输入控制受限等各种不确定因素,提出了一种基于动态面滤波法的自适应鲁棒位置控制器。对于模型中的不确定参数,采用投影算法进行有效估计,利用鲁棒滑模滤波器简化控制器的设计,引入一个辅助分析系统来对控制输入限制的影响进行有效分析,同时将辅助分析系统与反步方法结合,通过对模型的等价变换和选择适当的Lyapunov 函数,给出系统的自适应控制器的设计方法。仿真结果表明,该方法保证了系统的响应速度和控制精度,对参数摄动及外界负载扰动具有较强的鲁棒性。

WU Y F , MA D W , LE G G . Robust Adaptive backstepping control for rocket launcher position servo system with constraint control [J ] . Acta Armamentarii , 2013 , 34 ( 4 ): 477 - 483 . (in Chinese)

武冠群 , 宋申民 , 孙经广 . 考虑输入受限的航天器安全接近姿轨耦合控制 [J ] . 控制理论与应用 , 2018 , 35 ( 10 ): 1511 - 1520 .

WU G Q , SONG S M , SUN J G . Attitude and orbital coupled control of spcecraft safe approach considering input satturation [J ] . Control Theory and Application , 2018 , 35 ( 10 ): 1511 - 1520 . (in Chinese)

张春蕾 , 王立东 , 高闯 , 等 . 输入饱和及输出受限的纯反馈非线性系统控制 [J ] . 控制工程 , 2021 , 28 ( 3 ): 531 - 539 .

ZHANG C L , WANG L D , GAO C , et al. Pure feedback nonlinear system control with input saturation and output [J ] . Control Engineering of China , 2021 , 28 ( 3 ): 531 - 539 . (in Chinese)

段美君 , 周荻 . 控制量受限情况下的有限时间收敛制导律 [J ] . 兵工学报 , 2016 , 37 ( 6 ): 1030 - 1037 . DOI: 10.3969/j.issn.1000-1093.2016.06.009 http://doi.org/10.3969/j.issn.1000-1093.2016.06.009 针对动能拦截器拦截临近空间高速机动目标的问题，基于零化视线角速率原理，应用有限时间收敛理论推导出了控制量受限情况下的Bang-Bang型滑模制导律有限时间收敛条件,既适用于二维平面情况又适用于三维空间问题。通过设计制导律中滞环控制开关门限的上下限，在视线角速率可控的条件下去除了其抖振。仿真结果表明，制导律有限时间收敛，具有较高的制导精度，并对目标机动具有鲁棒性。

DUAN M J , ZHOU D . A guidance law with finite time under control variable constraint [J ] . Acta Armamentarii , 2016 , 37 ( 6 ): 1030 - 1037 . (in Chinese)

孙亮 , 马佳鹏 . 航天器输入受限的鲁棒自适应姿态跟踪控制 [J ] . 控制与决策 , 2021 , 36 ( 9 ): 2298 - 2304 .

SUN L , MA J P . Robust adaptive attitude tracking control of spacecraft with constrained inputs [J ] . Control and Decision , 2021 , 36 ( 9 ): 2298 - 2304 . (in Chinese)

丁岩 , 于志刚 . 考虑输入输出受限的无人机自适应滑模容错控制 [J ] . 系统工程与电子技术 , 2020 , 42 ( 10 ): 2340 - 2347 .

DING Y , YU Z G . Adaptive sliding mode fault tolerant control of UAV considering input and output constraints [J ] . Systems Engineering and Electronics , 2020 , 42 ( 10 ): 2340 - 2347 . (in Chinese)

WANG Y H , TONG H Y , REN H L . NESO-Based path following control for underactuated hovercrafts with unknown nonlinear uncertainties and a safety limit constraint [J ] . Applied Sciences , 2020 , 10 ( 15 ): 5287 . DOI: 10.3390/app10155287 http://doi.org/10.3390/app10155287 https://www.mdpi.com/2076-3417/10/15/5287 https://www.mdpi.com/2076-3417/10/15/5287 In this brief, the path following control problem of underactuated hovercrafts subject to nonlinear time-varying uncertainties and a safety limit constraint (SLC) is addressed. A novel homogenous nonlinear extended state observer (NESO)-based safe motion controller for a path following control scenario of underactuated hovercrafts is proposed. First, a NESO is constructed to estimate and compensate the nonlinear time-varying uncertainties for the underactuated hovercraft. Then, a NESO-based backstepping sliding mode control (BSMC) law with a turning SLC is proposed to achieve the yaw control for underactuated hovercrafts, which improves both safety and maneuverability of the underactuated hovercraft during the path following control scenario. The nonlinear time-varying turning SLC is first directly taken into the control system design, which is achieved by introducing an auxiliary dynamic system to limit the virtual input control during the backstepping design process. A NESO-based backstepping surge control law is also designed to achieve the surge control for underactuated hovercrafts. Furthermore, all error signals of the proposed closed-loop control system are proven to be bounded. Finally, an application case is tested on an underactuated hovercraft to illustrate the effectiveness and superiority of the designed control scheme.

AGHABABA M P , AKBARI M E . A chattering-free robust adaptive sliding mode controller for synchronization of two different chaotic systems with unknown uncertainties and external disturbances [J ] . Applied Mathematics and Computation , 2012 , 218 ( 9 ): 5757 - 5768 . DOI: 10.1016/j.amc.2011.11.080 http://doi.org/10.1016/j.amc.2011.11.080 https://linkinghub.elsevier.com/retrieve/pii/S0096300311014263 https://linkinghub.elsevier.com/retrieve/pii/S0096300311014263

高景波 . 基于超螺旋滑模变结构控制的R-AMD系统研究 [D ] . 大连 : 大连理工大学 , 2019 : 14 - 35 .

GAO J B . Super-Twisting Sliding Mode Control of R-AMD System [D ] . Dalian : Dalian University of Technology , 2019 : 14 - 35 . (in Chinese)

罗毅 , 王维 . 基于改进超螺旋算法的过热汽温滑模控制 [J ] . 动力工程学报 , 2020 , 40 ( 6 ): 475 - 480 . DOI: 10.19805/j.cnki.jcspe.2020.06.007 http://doi.org/10.19805/j.cnki.jcspe.2020.06.007 针对火电机组过热汽温被控对象的大惯性、大迟延及动态模型随负荷变化而变化等特性，将滑模变结构控制应用到串级过热汽温系统中。为了减小外部扰动带来的稳态误差和减弱滑模存在的抖振现象，引入积分环节，并采用改进超螺旋算法来代替切换控制，设计了一种新型滑模控制方法。同时在Simulink仿真工具下对过热汽温系统的高阶模型进行阶跃响应、模型参数失配和鲁棒性仿真试验。结果表明：与一般串级PID控制相比，本文方法的控制动态性能效果更好，调节时间和超调量得到显著改善，鲁棒性更强。

LUO Y , WANG W . Superheated steam temperature sliding mode control based on modified super-twisting algorithm [J ] . Journal of Chinese Society of Power Engineering , 2020 , 40 ( 6 ): 475 - 480 . (in Chinese)

姜佳林 . 基于超螺旋算法的直线电机扰动抑制研究 [D ] . 哈尔滨 : 哈尔滨工业大学 , 2019 : 12 - 37 .

JIANG J L . Disturbance suppression for linear motor based on super-twisting algorithm [J ] . Harbin : Harbin Institute of Technology , 2019 : 12 - 37 . (in Chinese)

WEI Y Y , LIU W K , DUAN G R . Missile guidance law with impact angle constraint and acceleration saturation [C ] //Proceedings of the 2016 35th Chinese Control Conference. Chengdu, China:IEEE , 2016 : 5340 - 5345 .

WANG Y H , TONG H Y , REN H L . NESO-based path following control for underactuated hovercrafts with unknown nonlinear uncertainties and a safety limit constraint [J ] . Applied Sciences , 2020 , 10 ( 15 ): 5287 . DOI: 10.3390/app10155287 http://doi.org/10.3390/app10155287 https://www.mdpi.com/2076-3417/10/15/5287 https://www.mdpi.com/2076-3417/10/15/5287 In this brief, the path following control problem of underactuated hovercrafts subject to nonlinear time-varying uncertainties and a safety limit constraint (SLC) is addressed. A novel homogenous nonlinear extended state observer (NESO)-based safe motion controller for a path following control scenario of underactuated hovercrafts is proposed. First, a NESO is constructed to estimate and compensate the nonlinear time-varying uncertainties for the underactuated hovercraft. Then, a NESO-based backstepping sliding mode control (BSMC) law with a turning SLC is proposed to achieve the yaw control for underactuated hovercrafts, which improves both safety and maneuverability of the underactuated hovercraft during the path following control scenario. The nonlinear time-varying turning SLC is first directly taken into the control system design, which is achieved by introducing an auxiliary dynamic system to limit the virtual input control during the backstepping design process. A NESO-based backstepping surge control law is also designed to achieve the surge control for underactuated hovercrafts. Furthermore, all error signals of the proposed closed-loop control system are proven to be bounded. Finally, an application case is tested on an underactuated hovercraft to illustrate the effectiveness and superiority of the designed control scheme.