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Journal articles on the topic 'Proxy based sliding mode control'

Author: Grafiati

Published: 4 June 2021

Last updated: 2 February 2022

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1

Kikuuwe, Ryo. "Some stability proofs on proxy-based sliding mode control." IMA Journal of Mathematical Control and Information 35, no. 4 (July 24, 2017): 1319–41. http://dx.doi.org/10.1093/imamci/dnx030.

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2

Zhao, Wei, Aiguo Song, and Yu Cao. "An Extended Proxy-Based Sliding Mode Control of Pneumatic Muscle Actuators." Applied Sciences 9, no. 8 (April 16, 2019): 1571. http://dx.doi.org/10.3390/app9081571.

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To solve the problem of controlling an intrinsically compliant actuator, pneumatic muscle actuator (PMA), this paper presents an extended proxy-based sliding mode control (EPSMC) strategy. It is well known that the chattering phenomenon of conventional sliding mode control (SMC) can be effectively solved by introducing a proxy between the physical object and desired position, which results in the so-called proxy-based sliding mode control (PSMC). To facilitate the theoretical analysis of PSMC and obtain a more general form of controller, a new virtual coupling and a SMC are used in our proposed EPSMC. For a class of second-order nonlinear system, the sufficient conditions ensuring the stability and passivity are obtained by using the Lyapunov functional method. Experiments on a real-time PMA control platform validate the effectiveness of the proposed method, and comparison studies also show the superiority of EPSMC over the conventional SMC, PSMC, and PID controllers.

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3

Van Damme, Michäel, Bram Vanderborght, Bjorn Verrelst, Ronald Van Ham, Frank Daerden, and Dirk Lefeber. "Proxy-based Sliding Mode Control of a Planar Pneumatic Manipulator." International Journal of Robotics Research 28, no. 2 (February 2009): 266–84. http://dx.doi.org/10.1177/0278364908095842.

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4

Kikuuwe, Ryo, Satoshi Yasukouchi, Hideo Fujimoto, and Motoji Yamamoto. "Proxy-Based Sliding Mode Control: A Safer Extension of PID Position Control." IEEE Transactions on Robotics 26, no. 4 (August 2010): 670–83. http://dx.doi.org/10.1109/tro.2010.2051188.

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5

Gu, Guo-Ying, Li-Min Zhu, Chun-Yi Su, Han Ding, and Sergej Fatikow. "Proxy-Based Sliding-Mode Tracking Control of Piezoelectric-Actuated Nanopositioning Stages." IEEE/ASME Transactions on Mechatronics 20, no. 4 (August 2015): 1956–65. http://dx.doi.org/10.1109/tmech.2014.2360416.

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6

Prieto, Pablo J., Ernesto Rubio, Luis Hernández, and Orlando Urquijo. "Proxy-based sliding mode control on platform of 3 degree of freedom (3-DOF)." Advanced Robotics 27, no. 10 (July 2013): 773–84. http://dx.doi.org/10.1080/01691864.2013.785471.

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7

Al-Shuka, Hayder F. N. "Proxy-Based Sliding Mode Vibration Control with an Adaptive Approximation Compensator for Euler-Bernoulli Smart Beams." Journal Européen des Systèmes Automatisés 53, no. 6 (December 23, 2020): 825–34. http://dx.doi.org/10.18280/jesa.530608.

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Proxy-based sliding mode control PSMC is an improved version of PID control that combines the features of PID and sliding mode control SMC with continuously dynamic behaviour. However, the stability of the control architecture maybe not well addressed. Consequently, this work is focused on modification of the original version of the proxy-based sliding mode control PSMC by adding an adaptive approximation compensator AAC term for vibration control of an Euler-Bernoulli beam. The role of the AAC term is to compensate for unmodelled dynamics and make the stability proof more easily. The stability of the proposed control algorithm is systematically proved using Lyapunov theory. Multi-modal equation of motion is derived using the Galerkin method. The state variables of the multi-modal equation are expressed in terms of modal amplitudes that should be regulated via the proposed control system. The proposed control structure is implemented on a simply supported beam with two piezo-patches. The simulation experiments are performed using MATLAB/SIMULINK package. The locations of piezo-transducers are optimally placed on the beam. A detailed comparison study is implemented including three scenarios. Scenario 1 includes disturbing the smart beam while no feedback loop is established (open-loop system). In scenario 2, a PD controller is applied on the vibrating beam. Whereas, scenario 3 includes implementation of the PSMC+AAC. For all previously mentioned scenarios, two types of disturbances are applied separately: 1) an impulse force of 1 N peak and 1 s pulse width, and 2) a sinusoidal disturbance with 0.5 N amplitude and 20 Hz frequency. For impulse disturbance signals, the results show the superiority of the PSMC+AAC in comparison with the conventional PD control. Whereas, both the PSMC+ACC and the PD control work well in the case of a sinusoidal disturbance signal and the superiority of the PSMC is not clear.

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8

Chen, Geng, Zhihao Zhou, Bram Vanderborght, Ninghua Wang, and Qining Wang. "Proxy-based sliding mode control of a robotic ankle-foot system for post-stroke rehabilitation." Advanced Robotics 30, no. 15 (May 4, 2016): 992–1003. http://dx.doi.org/10.1080/01691864.2016.1176601.

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9

Huang, Ming, Xinhan Huang, Xikai Tu, Zefang Li, and Yue Wen. "An online gain tuning proxy-based sliding mode control using neural network for a gait training robotic orthosis." Cluster Computing 19, no. 4 (September 17, 2016): 1987–2000. http://dx.doi.org/10.1007/s10586-016-0629-y.

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10

Zhao, Wei, and Aiguo Song. "Active Motion Control of a Knee Exoskeleton Driven by Antagonistic Pneumatic Muscle Actuators." Actuators 9, no. 4 (December 10, 2020): 134. http://dx.doi.org/10.3390/act9040134.

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The pneumatic muscle actuator (PMA) has been widely applied in the researches of rehabilitation robotic devices for its high power to weight ratio and intrinsic compliance in the past decade. However, the high nonlinearity and hysteresis behavior of PMA limit its practical application. Hence, the control strategy plays an important role in improving the performance of PMA for the effectiveness of rehabilitation devices. In this paper, a PMA-based knee exoskeleton based on ergonomics is proposed. Based on the designed knee exoskeleton, a novel proxy-based sliding mode control (PSMC) is introduced to obtain the accurate trajectory tracking. Compared with conventional control approaches, this new PSMC can obtain better performance for the designed PMA-based exoskeleton. Experimental results indicate good tracking performance of this controller, which provides a good foundation for the further development of assist-as-needed training strategies in gait rehabilitation.

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11

Su, Chen, Ao Chai, Xikai Tu, Hongyu Zhou, Haiqiang Wang, Zufang Zheng, Jingyan Cao, and Jiping He. "Passive and Active Control Strategies of a Leg Rehabilitation Exoskeleton Powered by Pneumatic Artificial Muscles." International Journal of Pattern Recognition and Artificial Intelligence 31, no. 10 (March 9, 2017): 1759021. http://dx.doi.org/10.1142/s0218001417590212.

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Nerve injury can cause lower limb paralysis and gait disorder. Currently lower limb rehabilitation exoskeleton robots used in the hospitals need more power to correct abnormal motor patterns of stroke patients’ legs. These gait rehabilitation robots are powered by cumbersome and bulky electric motors, which provides a poor user experience. A newly developed gait rehabilitation exoskeleton robot actuated by low-cost and lightweight pneumatic artificial muscles (PAMs) is presented in this research. A model-free proxy-based sliding mode control (PSMC) strategy and a model-based chattering mitigation robust variable control (CRVC) strategy were developed and first applied in rehabilitation trainings, respectively. As the dynamic response of PAM due to the compressed air is low, an innovative intention identification control strategy was taken in active trainings by the use of the subject’s intention indirectly through the estimation of the interaction force between the subject’s leg and the exoskeleton. The proposed intention identification strategy was verified by treadmill-based gait training experiments.

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12

Cao, Yu, Jian Huang, Zhangbo Huang, Xikai Tu, and Samer Mohammed. "Optimizing Control of Passive Gait Training Exoskeleton Driven by Pneumatic Muscles Using Switch-Mode Firefly Algorithm." Robotica 37, no. 12 (April 22, 2019): 2087–103. http://dx.doi.org/10.1017/s0263574719000511.

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SummaryThis paper presents a lower-limb exoskeleton that is actuated by pneumatic muscle actuators (PMAs). This exoskeleton system is composed of the mechanical structures, a treadmill, and a weight support system. With the cooperative work of the three parts, the system aims to assist either the elderly for muscle strengthening by conducting walking activities or the stroke patients during a rehabilitation training program. A mechanism is developed to separate the PMAs from the wearer’s legs to reduce the subject’s physical exertion. Furthermore, considering the difficulty in the modeling of proposed PMAs-driven exoskeleton, a safe and model-free control strategy called proxy-based sliding mode control (PSMC) is used to ensure proper control of the exoskeleton. However, the favorable performances are strongly dependent on the appropriate control parameters, which may be difficult to obtain with blind tuning. Therefore, we propose a global parameters optimization algorithm called switch-mode firefly algorithm (SMFA) to automatically calculate the pre-defined object function and attain the most applicable parameters. Experimental studies are conducted, and the results show the effectiveness of the proposed method.

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13

Huo, Weiguang, Victor Arnez-Paniagua, Guangzheng Ding, Yacine Amirat, and Samer Mohammed. "Adaptive Proxy-Based Controller of an Active Ankle Foot Orthosis to Assist Lower Limb Movements of Paretic Patients." Robotica 37, no. 12 (March 18, 2019): 2147–64. http://dx.doi.org/10.1017/s0263574719000250.

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SummaryThis paper deals with the control of an active ankle foot orthosis (AAFO) for paretic patients. State of the art methods using an AAFO try to track a predefined trajectory of the ankle joint while guaranteeing the wearer’s safety in the presence of a large tracking error. Combining the wearer’s safety and tracking accuracy is generally difficult to achieve at the same time, hence a trade-off should be found. Proxy-based sliding mode control (PSMC) offers great performances in both position tracking and safety guarantee. However, its tracking performance is subject to the influences of parameter uncertainties and external disturbances that generally occur during walking. This paper introduces an adaptation interaction method to the basic PSMC with an online adaptation of the proportional, integral and derivative parameters. At the same time, a gait phase-based ankle reference generation algorithm was proposed to adjust the joint reference trajectory in real time. The experiments using the AAFO show better tracking results with respect to basic PSMC while guaranteeing the safety.

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14

Beyl, Pieter, Michaël Van Damme, Ronald Van Ham, Bram Vanderborght, and Dirk Lefeber. "Design and Control of a Lower Limb Exoskeleton for Robot-Assisted Gait Training." Applied Bionics and Biomechanics 6, no. 2 (2009): 229–43. http://dx.doi.org/10.1155/2009/580734.

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Robot-assisted rehabilitation of gait still faces many challenges, one of which is improving physical human-robot interaction. The use of pleated pneumatic artificial muscles to power a step rehabilitation robot has the potential to meet this challenge. This paper reports on the development of a gait rehabilitation exoskeleton with a knee joint powered by pleated pneumatic artificial muscles. It is intended as a platform for the evaluation of design and control concepts in view of improved physical human-robot interaction. The design was focused on the optimal dimensioning of the actuator configuration. Safety being the most important prerequisite, a proxy-based sliding mode controller (PSMC) was implemented as it combines accurate tracking during normal operation with a smooth, slow and safe recovery from large position errors. Treadmill walking experiments of a healthy subject wearing the powered exoskeleton show the potential of PSMC as a safe robot-in-charge control strategy for robot-assisted gait training.

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15

Laghrouche, Salah, Franck Plestan, and Alain Glumineau. "Higher order sliding mode control based on integral sliding mode." Automatica 43, no. 3 (March 2007): 531–37. http://dx.doi.org/10.1016/j.automatica.2006.09.017.

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16

Zhao, Dongya, Ge Zhao, Shaoyuan Li, and Quanmin Zhu. "Observer based terminal sliding mode control." IFAC Proceedings Volumes 46, no. 13 (2013): 178–81. http://dx.doi.org/10.3182/20130708-3-cn-2036.00035.

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17

HIKITA, H. "Servomechanisms based on sliding mode control." International Journal of Control 48, no. 2 (August 1988): 435–47. http://dx.doi.org/10.1080/00207178808906189.

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18

Iglesias, E., Y. García, M. Sanjuan, O. Camacho, and C. Smith. "Fuzzy surface-based sliding mode control." ISA Transactions 46, no. 1 (February 2007): 73–83. http://dx.doi.org/10.1016/j.isatra.2006.04.002.

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19

Laghrouche, S., F. Plestan, and A. Glumineau. "Higher order sliding mode control based on optimal LQ control and integral sliding mode." IFAC Proceedings Volumes 37, no. 13 (September 2004): 597–602. http://dx.doi.org/10.1016/s1474-6670(17)31289-2.

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20

Fei, Y. N., J. S. Smith, and Q. H. Wu. "Sliding Mode Control of Robot Manipulators Based on Sliding Mode Perturbation Observation." Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering 220, no. 3 (May 2006): 201–10. http://dx.doi.org/10.1243/09596518jsce93.

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21

Tang, W. Q., and Y. L. Cai. "High-order sliding mode control design based on adaptive terminal sliding mode." International Journal of Robust and Nonlinear Control 23, no. 2 (October 14, 2011): 149–66. http://dx.doi.org/10.1002/rnc.1820.

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22

Bahraini, Masoud, Mohammad Javad Yazdanpanah, Shokufeh Vakili, and Mohammad Reza Jahed-Motlagh. "Sliding mode control revisited." Transactions of the Institute of Measurement and Control 42, no. 14 (June 8, 2020): 2698–707. http://dx.doi.org/10.1177/0142331220924861.

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Controller design for nonlinear systems in its general form is complicated and an open problem. Finding a solution to this problem becomes more complicated when unwanted terms, such as disturbance, are taken into account. To provide a robust design for a subclass of nonlinear systems, sliding mode controllers (SMCs) are used. These controllers have a systematic design procedure and can reject bounded disturbances and at the same time guarantee stability. The guaranteed stability is achieved by separating system states into two parts and assuming that the input to state stability (ISS) condition holds for internal dynamics. This condition restricts the applicability of the SMC and limits the system performance when the controller is designed based on that. In order to remove this restriction and improve the performance, the ISS condition has been relaxed in this study. The relaxation is performed by redesigning SMCs based on suggested Lyapunov functions. The proposed idea insures global asymptotic stability of the closed loop system and is used to revise different well-known SMCs such as conventional SMC, terminal SMC, non-singular terminal SMC, integral SMC, super-twisting SMC, and super-twisting integral SMC. Comparisons between conventional and revised versions are made using simulation to demonstrate excellence of the revisited controllers.

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23

Feng, Chieh Chuan, Li Peng Yin, and En Chih Chang. "Robust Control Design Based-On Integral Sliding-Mode Control." Applied Mechanics and Materials 284-287 (January 2013): 2301–4. http://dx.doi.org/10.4028/www.scientific.net/amm.284-287.2301.

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This paper proposes a robust control design based-on integral sliding-mode and H2–norm performance criterion to handle a class of time-varying systems with perturbations including non-linearities and disturbances. The stabilization problems for such systems are studied: integral slid-ing-mode is designated to completely nullify the matched perturbations and, in the meantime, elim-inate the reaching phase to the sliding surface, while H2–norm is a robust linear control measured for system on the sliding surface. In addition to the integral sliding mode control, the contribution of the paper is to implement a parameter-dependent Lyapunov function for H2–norm robust linear control that the overall designed system is less conservative for the system with both matched and unmatched perturbations.

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24

Choi, Han-Ho. "Reduced Order Observer Based Sliding Mode Control." Journal of Control, Automation and Systems Engineering 12, no. 11 (November 1, 2006): 1057–60. http://dx.doi.org/10.5302/j.icros.2006.12.11.1057.

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25

Camacho, Oscar. "A PREDICTIVE APPROACH BASED-SLIDING MODE CONTROL." IFAC Proceedings Volumes 35, no. 1 (2002): 381–85. http://dx.doi.org/10.3182/20020721-6-es-1901.00632.

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26

Taimoor, Muhammad, Li Aijun, and Rooh ul Amin. "Disturbances rejection based on sliding mode control." Aircraft Engineering and Aerospace Technology 91, no. 4 (April 1, 2019): 680–99. http://dx.doi.org/10.1108/aeat-04-2018-0121.

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Purpose The purpose of this paper aims to investigate an effective algorithm for different types of disturbances rejection. New dynamics are designed based on disturbance. Observer-based sliding mode control (SMC) technique is used for approximation the disturbances as well as to stabilize the system effectively in presence of uncertainties. Design/methodology/approach This research work investigates the disturbances rejection algorithm for fixed-wing unmanned aerial vehicle. An algorithm based on SMC is introduced for disturbances rejection. Two types of disturbances are considered, the constant disturbance and the sinusoidal disturbance. The comprehensive lateral and longitudinal models of the system are presented. Two types of dynamics, the dynamics without disturbance and the new dynamics with disturbance, are presented. An observer-based algorithm is presented for the estimation of the dynamics with disturbances. Intensive simulations and experiments have been performed; the results not only guarantee the robustness and stability of the system but the effectiveness of the proposed algorithm as well. Findings In previous research work, new dynamics based on disturbances rejection are not investigated in detail; in this research work both the lateral and longitudinal dynamics with different disturbances are investigated. Practical implications As the stability is always important for flight, so the algorithm proposed in this research guarantees the robustness and rejection of disturbances, which plays a vital role in practical life for avoiding any kind of damage. Originality/value In the previous research work, new dynamics based on disturbances rejection are not investigated in detail; in this research work both the lateral and longitudinal dynamics with different disturbances are investigated. An observer-based SMC not only approximates the different disturbances and also these disturbances are rejected in order to guarantee the effectiveness and robustness.

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27

Castro-Linares, R., A. Glumineau, S. Laghrouche, and F. Plestan. "Higher Order Sliding Mode Observer-Based Control." IFAC Proceedings Volumes 37, no. 21 (December 2004): 481–86. http://dx.doi.org/10.1016/s1474-6670(17)30515-3.

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28

Almakhles, Dhafer. "Sliding mode control as binary‐based quantizers." Asian Journal of Control 22, no. 3 (February 13, 2019): 1090–98. http://dx.doi.org/10.1002/asjc.2052.

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29

Lu, Z., S. Kawamura, and A. A. Goldenburg. "An approach to sliding-mode based control." IEEE Transactions on Robotics and Automation 11, no. 5 (1995): 754–59. http://dx.doi.org/10.1109/70.466608.

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30

Obeid, Hussein, Leonid M. Fridman, Salah Laghrouche, and Mohamed Harmouche. "Barrier function-based adaptive sliding mode control." Automatica 93 (July 2018): 540–44. http://dx.doi.org/10.1016/j.automatica.2018.03.078.

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31

Liang, Yanyang, Shuang Cong, and Weiwei Shang. "Function approximation-based sliding mode adaptive control." Nonlinear Dynamics 54, no. 3 (January 25, 2008): 223–30. http://dx.doi.org/10.1007/s11071-007-9324-0.

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32

Taleb, M., F. Plestan, and B. Bououlid. "Higher order sliding mode control based on adaptive first order sliding mode controller." IFAC Proceedings Volumes 47, no. 3 (2014): 1380–85. http://dx.doi.org/10.3182/20140824-6-za-1003.02487.

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33

Wang, Liang, Yongzhi Sheng, and Xiangdong Liu. "A novel adaptive high-order sliding mode control based on integral sliding mode." International Journal of Control, Automation and Systems 12, no. 3 (May 10, 2014): 459–72. http://dx.doi.org/10.1007/s12555-013-0361-9.

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34

Adamiak, Katarzyna. "Reference Sliding Variable Based Chattering-Free Quasi-Sliding Mode Control." IEEE Access 8 (2020): 133086–94. http://dx.doi.org/10.1109/access.2020.3010900.

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35

Fallaha, Charles, and Maarouf Saad. "Model-based sliding functions design for sliding mode robot control." International Journal of Modelling, Identification and Control 30, no. 1 (2018): 48. http://dx.doi.org/10.1504/ijmic.2018.10014595.

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36

Zong, Q., J. Zhang, and Z. S. Zhao. "Higher order sliding mode control with self-tuning law based on integral sliding mode." IET Control Theory & Applications 4, no. 7 (July 1, 2010): 1282–89. http://dx.doi.org/10.1049/iet-cta.2008.0610.

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37

Ma, Ding. "Duffing Chaotic System Stability Control Based on Sliding Mode Control." Advanced Materials Research 605-607 (December 2012): 1639–42. http://dx.doi.org/10.4028/www.scientific.net/amr.605-607.1639.

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Considering the Duffing chaotic system, the problem of stability control based on the terminal sliding mode variable structure is studied. A new terminal sliding mode surface and control law are designed. On this basis, the stability of closed-loop system is analyzed. Simulation results show the effectiveness of the control method.

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38

Chegini, Somayeh, and Majid Yarahmadi. "Quantum sliding mode control via error sliding surface." Journal of Vibration and Control 24, no. 22 (January 15, 2018): 5345–52. http://dx.doi.org/10.1177/1077546317752848.

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In this paper, a new quantum sliding mode control, for improving the performance of the two-level quantum sliding mode control systems with bounded uncertainties, is introduced. The presented quantum sliding surface is based on the error which occurs between the predetermined sliding mode and the system state. The control objective is to derive the system state to reach the sliding mode domain and then maintain its motion on it. For this purpose, we use the sliding mode control method and periodic projective measurements. A theorem for facilitating the presented method is proved. The simulated example shows that both the reaching time to the sliding mode and the control amplitude are significantly decreased, which demonstrate the effectiveness and validity of the presented method.

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39

KOCAOĞLU, Aykut, and Cüneyt GÜZELİŞ. "Model-based robust chaotification using sliding mode control." TURKISH JOURNAL OF ELECTRICAL ENGINEERING & COMPUTER SCIENCES 22 (2014): 940–56. http://dx.doi.org/10.3906/elk-1210-132.

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40

Sarraf, Elie H., Mrigank Sharma, and Edmond Cretu. "Novel sliding mode control for MEMS-based resonators." Procedia Engineering 25 (2011): 1305–8. http://dx.doi.org/10.1016/j.proeng.2011.12.322.

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41

Kurkcu, Burak, Cosku Kasnakoglu, and Mehmet Onder Efe. "Disturbance/Uncertainty Estimator Based Integral Sliding-Mode Control." IEEE Transactions on Automatic Control 63, no. 11 (November 2018): 3940–47. http://dx.doi.org/10.1109/tac.2018.2808440.

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42

Lu, Y.-S. "Sliding-mode control based on internal model principle." Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering 221, no. 3 (May 2007): 395–406. http://dx.doi.org/10.1243/09596518jsce98.

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43

Ackermann, J., and V. Utkin. "Sliding mode control design based on Ackermann's formula." IEEE Transactions on Automatic Control 43, no. 2 (1998): 234–37. http://dx.doi.org/10.1109/9.661072.

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44

Hussaini, M. Mohammadha, and R. Anita. "Robust Sliding mode control based wind power generation." i-manager's Journal on Electrical Engineering 3, no. 2 (December 15, 2009): 65–70. http://dx.doi.org/10.26634/jee.3.2.1050.

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45

Xiao, Lingfei, and Yue Zhu. "Passivity-based Integral Sliding Mode Active Suspension Control." IFAC Proceedings Volumes 47, no. 3 (2014): 5205–10. http://dx.doi.org/10.3182/20140824-6-za-1003.00536.

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46

Li, Hong Ru, and Zhi Bin Jiang. "CMAC-Based Backstepping Sliding Mode Control of PMSM." Applied Mechanics and Materials 380-384 (August 2013): 480–84. http://dx.doi.org/10.4028/www.scientific.net/amm.380-384.480.

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The paper describes a hybrid approach to the problem of controlling permanent magnet synchronous motor (PMSM) with unmodelled dynamics and unknown external disturbances. First, the backstepping sliding mode (BS) controller based on the equation of PMSM is elaborated. Its effect is to achieve a stable control. Then the cerebellar model arithmetic computer (CMAC) controller is implemented to compensate uncertainties. Furthermore, the nonlinear disturbance observer (DO) is applied to estimate the time-varying lumped disturbance D(t) for improving the precision of the tracking control. The proposed CMAC-based method can acquire high control performance in the presence of disturbance and guarantee the stability of closed-loop systems on the basis of the Lyapunov theorem. The effectiveness and robustness are demonstrated through simulation results obtained for the tracking control of PMSM.

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47

Koshkouei, Ali J. "Passivity-based sliding mode control for nonlinear systems." International Journal of Adaptive Control and Signal Processing 22, no. 9 (November 2008): 859–74. http://dx.doi.org/10.1002/acs.1028.

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48

Incremona, Gian Paolo, and Antonella Ferrara. "Adaptive model-based event-triggered sliding mode control." International Journal of Adaptive Control and Signal Processing 30, no. 8-10 (January 14, 2016): 1298–316. http://dx.doi.org/10.1002/acs.2665.

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49

Béthoux, O., J. P. Barbot, and M. Hilairet. "Multicell actuator based on a sliding mode control." European Physical Journal Applied Physics 43, no. 2 (July 17, 2008): 217–23. http://dx.doi.org/10.1051/epjap:2008121.

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50

Knight, M. J., R. Sutton, and R. S. Burns. "Fuzzy model based integral action sliding mode control." Soft Computing - A Fusion of Foundations, Methodologies and Applications 7, no. 4 (February 1, 2003): 244–51. http://dx.doi.org/10.1007/s00500-002-0211-9.

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