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1

Prokhorov, D. V., and D. C. Wunsch. "Adaptive critic designs." IEEE Transactions on Neural Networks 8, no. 5 (September 1997): 997–1007. http://dx.doi.org/10.1109/72.623201.

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2

Prokhorov, D. V., and D. C. Wunsch. "Corrections To "Adaptive Critic Designs"." IEEE Transactions on Neural Networks 8, no. 6 (November 1997): 1563. http://dx.doi.org/10.1109/tnn.1997.641481.

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3

Prokhorov, Danil V., Roberto A. Santiago, and Donald C. Wunsch. "Adaptive critic designs: A case study for neurocontrol." Neural Networks 8, no. 9 (January 1995): 1367–72. http://dx.doi.org/10.1016/0893-6080(95)00042-9.

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4

Mohagheghi, Salman, Ganesh K. Venayagamoorthy, and Ronald G. Harley. "Fully Evolvable Optimal Neurofuzzy Controller Using Adaptive Critic Designs." IEEE Transactions on Fuzzy Systems 16, no. 6 (December 2008): 1450–61. http://dx.doi.org/10.1109/tfuzz.2008.925910.

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5

Govindhasamy, James J., Seán F. McLoone, George W. Irwin, John J. French, and Richard P. Doyle. "Reinforcement Learning for Online Industrial Process Control." Journal of Advanced Computational Intelligence and Intelligent Informatics 9, no. 1 (January 20, 2005): 23–30. http://dx.doi.org/10.20965/jaciii.2005.p0023.

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Reinforcement learning, in the form of Adaptive Critic Designs (ACDs), have the ability to analyse or evaluate a situation and respond to it accordingly. They offer an excellent alternative for adaptively controlling and optimising the highly nonlinear processes found in industry. Here, an enhanced implementation of the action dependent adaptive critic design (ADAC) of Si and Wang [9] is investigated for modelling and control of an industrial grinding process used in the manufacture of hard disk drive platters. This study, one of the first reported industrial applications of this emerging technology, shows that the proposed ADAC control scheme can achieve a 33% reduction in platter rejects compared to an existing proprietary controller.
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6

Deb, Alok Kanti, Jayadeva, Madan Gopal, and Suresh Chandra. "SVM-Based Tree-Type Neural Networks as a Critic in Adaptive Critic Designs for Control." IEEE Transactions on Neural Networks 18, no. 4 (July 2007): 1016–30. http://dx.doi.org/10.1109/tnn.2007.899255.

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7

Hendzel, Zenon, and Marcin Szuster. "Discrete Action Dependant Heuristic Dynamic Programming in Control of a Wheeled Mobile Robot." Solid State Phenomena 164 (June 2010): 419–24. http://dx.doi.org/10.4028/www.scientific.net/ssp.164.419.

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In presented paper we propose a discrete tracking control algorithm for a two-wheeled mobile robot. The control algorithm consists of discrete Adaptive Critic Design (ACD) in Action Dependant Heuristic Dynamic Programming (ADHDP) configuration, PD controller and a supervisory term, derived from the Lyapunov stability theorem and based on the variable structure systems theory. Adaptive Critic Designs are a group of algorithms that use two independent structures for estimation of optimal value function from Bellman equation and estimation of optimal control law. ADHDP algorithm consists of Actor (ASE - Associate Search Element) that estimates the optimal control law and Critic (ACE - Adaptive Critic Element) that evaluates quality of control by estimation of the optimal value function from Bellman equation. Both structures are realized in a form of Neural Networks (NN). ADHDP algorithm does not require a plant model (the wheeled mobile robot (WMR) model) for ACE or ASE neural network weights update procedure (in contrast with other ACD configurations e.g. Heuristic Dynamic Programming or Dual Heuristic Programming that use the plant model). In presented control algorithm Actor-Critic structure is supported by PD controller and the supervisory term, that guarantee stable implementation of tracking in an initial adaptive critic neural networks learning phase, and robustness in a face of disturbances. Verification of proposed control algorithm was realized on the two-wheeled mobile robot Pioneer-2DX.
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8

Liu, Derong, and H. Daniel Patiño. "A self-learning ship steering controller based on adaptive Critic Designs." IFAC Proceedings Volumes 32, no. 2 (July 1999): 5070–75. http://dx.doi.org/10.1016/s1474-6670(17)56863-9.

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9

Xin Xu, Zhongsheng Hou, Chuanqiang Lian, and Haibo He. "Online Learning Control Using Adaptive Critic Designs With Sparse Kernel Machines." IEEE Transactions on Neural Networks and Learning Systems 24, no. 5 (May 2013): 762–75. http://dx.doi.org/10.1109/tnnls.2012.2236354.

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10

Yang, Xiong, and Qinglai Wei. "Adaptive Critic Designs for Optimal Event-Driven Control of a CSTR System." IEEE Transactions on Industrial Informatics 17, no. 1 (January 2021): 484–93. http://dx.doi.org/10.1109/tii.2020.2972383.

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11

Iyer, M. S., and D. C. Wunsch. "Dynamic re-optimization of a fed-batch fermentor using adaptive critic designs." IEEE Transactions on Neural Networks 12, no. 6 (2001): 1433–44. http://dx.doi.org/10.1109/72.963778.

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12

Yang, Xiong, and Haibo He. "Adaptive critic designs for optimal control of uncertain nonlinear systems with unmatched interconnections." Neural Networks 105 (September 2018): 142–53. http://dx.doi.org/10.1016/j.neunet.2018.05.005.

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13

Wang, Ding, Derong Liu, Qichao Zhang, and Dongbin Zhao. "Data-Based Adaptive Critic Designs for Nonlinear Robust Optimal Control With Uncertain Dynamics." IEEE Transactions on Systems, Man, and Cybernetics: Systems 46, no. 11 (November 2016): 1544–55. http://dx.doi.org/10.1109/tsmc.2015.2492941.

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14

Yang, Xiong, and Haibo He. "Adaptive Critic Designs for Event-Triggered Robust Control of Nonlinear Systems With Unknown Dynamics." IEEE Transactions on Cybernetics 49, no. 6 (June 2019): 2255–67. http://dx.doi.org/10.1109/tcyb.2018.2823199.

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15

Radac and Precup. "Data-Driven Model-Free Tracking Reinforcement Learning Control with VRFT-based Adaptive Actor-Critic." Applied Sciences 9, no. 9 (April 30, 2019): 1807. http://dx.doi.org/10.3390/app9091807.

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This paper proposes a neural network (NN)-based control scheme in an Adaptive Actor-Critic (AAC) learning framework designed for output reference model tracking, as a representative deep-learning application. The control learning scheme is model-free with respect to the process model. AAC designs usually require an initial controller to start the learning process; however, systematic guidelines for choosing the initial controller are not offered in the literature, especially in a model-free manner. Virtual Reference Feedback Tuning (VRFT) is proposed for obtaining an initially stabilizing NN nonlinear state-feedback controller, designed from input-state-output data collected from the process in open-loop setting. The solution offers systematic design guidelines for initial controller design. The resulting suboptimal state-feedback controller is next improved under the AAC learning framework by online adaptation of a critic NN and a controller NN. The mixed VRFT-AAC approach is validated on a multi-input multi-output nonlinear constrained coupled vertical two-tank system. Discussions on the control system behavior are offered together with comparisons with similar approaches.
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16

Al-Tamimi, Asma, Murad Abu-Khalaf, and Frank L. Lewis. "Adaptive Critic Designs for Discrete-Time Zero-Sum Games With Application to $H_{\infty}$ Control." IEEE Transactions on Systems, Man and Cybernetics, Part B (Cybernetics) 37, no. 1 (February 2007): 240–47. http://dx.doi.org/10.1109/tsmcb.2006.880135.

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17

Yang, Xiong, and Haibo He. "Event-Triggered Robust Stabilization of Nonlinear Input-Constrained Systems Using Single Network Adaptive Critic Designs." IEEE Transactions on Systems, Man, and Cybernetics: Systems 50, no. 9 (September 2020): 3145–57. http://dx.doi.org/10.1109/tsmc.2018.2853089.

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18

Liang, Yuling, Huaguang Zhang, Kun Zhang, and Rui Wang. "A novel neural network discrete‐time optimal control design for nonlinear time‐delay systems using adaptive critic designs." Optimal Control Applications and Methods 41, no. 3 (February 20, 2020): 748–64. http://dx.doi.org/10.1002/oca.2567.

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19

WEI, Qing-Lai, Hua-Guang ZHANG, and Li-Li CUI. "Data-based Optimal Control for Discrete-time Zero-sum Games of 2-D Systems Using Adaptive Critic Designs." Acta Automatica Sinica 35, no. 6 (August 14, 2009): 682–92. http://dx.doi.org/10.3724/sp.j.1004.2009.00682.

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20

WEI, Qing-Lai, Hua-Guang ZHANG, and Li-Li CUI. "Data-based Optimal Control for Discrete-time Zero-sum Games of 2-D Systems Using Adaptive Critic Designs." Acta Automatica Sinica 35, no. 6 (June 2009): 682–92. http://dx.doi.org/10.1016/s1874-1029(08)60091-9.

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21

Wang, Wei, Xin Chen, and Jianxin He. "Adaptive Critic Design with Local Gaussian Process Models." Journal of Advanced Computational Intelligence and Intelligent Informatics 20, no. 7 (December 20, 2016): 1135–40. http://dx.doi.org/10.20965/jaciii.2016.p1135.

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In this paper, local Gaussian process (GP) approximation is introduced to build the critic network of adaptive dynamic programming (ADP). The sample data are partitioned into local regions, and for each region, an individual GP model is utilized. The nearest local model is used to predict a given state-action point. With the two-phase value iteration method for a Gaussian-kernel (GK)-based critic network which realizes the update of the hyper-parameters and value functions simultaneously, fast value function approximation can be achieved. Combining this critic network with an actor network, we present a local GK-based ADP approach. Simulations were carried out to demonstrate the feasibility of the proposed approach.
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22

Kuljaca, Ognjen, and Frank L. Lewis. "Adaptive critic design using non-linear network structures." International Journal of Adaptive Control and Signal Processing 17, no. 6 (2003): 431–45. http://dx.doi.org/10.1002/acs.760.

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23

Herzallah, Randa, and Miroslav Kárný. "Fully probabilistic control design in an adaptive critic framework." Neural Networks 24, no. 10 (December 2011): 1128–35. http://dx.doi.org/10.1016/j.neunet.2011.06.006.

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24

Shelton, Robert O., and James K. Peterson. "Controlling a truck with an adaptive critic CMAC design." SIMULATION 58, no. 5 (May 1992): 319–26. http://dx.doi.org/10.1177/003754979205800504.

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25

Gurrala, G., I. Sen, and R. Padhi. "Single network adaptive critic design for power system stabilisers." IET Generation, Transmission & Distribution 3, no. 9 (September 1, 2009): 850–58. http://dx.doi.org/10.1049/iet-gtd.2009.0023.

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26

Chen, Xin, Penghuan Xie, Yonghua Xiong, Yong He, and Min Wu. "Two-Phase Iteration for Value Function Approximation and Hyperparameter Optimization in Gaussian-Kernel-Based Adaptive Critic Design." Mathematical Problems in Engineering 2015 (2015): 1–14. http://dx.doi.org/10.1155/2015/760459.

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Adaptive Dynamic Programming (ADP) with critic-actor architecture is an effective way to perform online learning control. To avoid the subjectivity in the design of a neural network that serves as a critic network, kernel-based adaptive critic design (ACD) was developed recently. There are two essential issues for a static kernel-based model: how to determine proper hyperparameters in advance and how to select right samples to describe the value function. They all rely on the assessment of sample values. Based on the theoretical analysis, this paper presents a two-phase simultaneous learning method for a Gaussian-kernel-based critic network. It is able to estimate the values of samples without infinitively revisiting them. And the hyperparameters of the kernel model are optimized simultaneously. Based on the estimated sample values, the sample set can be refined by adding alternatives or deleting redundances. Combining this critic design with actor network, we present a Gaussian-kernel-based Adaptive Dynamic Programming (GK-ADP) approach. Simulations are used to verify its feasibility, particularly the necessity of two-phase learning, the convergence characteristics, and the improvement of the system performance by using a varying sample set.
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27

Cheng, B., R. J. Stanley, W. V. Stoecker, and K. Hinton. "Automatic telangiectasia analysis in dermoscopy images using adaptive critic design." Skin Research and Technology 18, no. 4 (December 5, 2011): 389–96. http://dx.doi.org/10.1111/j.1600-0846.2011.00584.x.

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28

Lee, Hanna, Seong-hun Kim, and Youdan Kim. "Actor-Critic-Based Optimal Adaptive Control Design for Morphing Aircraft." IFAC-PapersOnLine 53, no. 2 (2020): 14863–68. http://dx.doi.org/10.1016/j.ifacol.2020.12.1943.

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29

Yang, Baosheng, and Deguang Cao. "Action-Dependent Adaptive Critic Design Based Neurocontroller for Cement Precalciner Kiln." International Journal of Computer Network and Information Security 1, no. 1 (October 18, 2009): 60–67. http://dx.doi.org/10.5815/ijcnis.2009.01.08.

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30

Chen, Xin, Wei Wang, Weihua Cao, and Min Wu. "Gaussian-kernel-based adaptive critic design using two-phase value iteration." Information Sciences 482 (May 2019): 139–55. http://dx.doi.org/10.1016/j.ins.2018.12.019.

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31

Zhao Sun, Xi Chen, and Zhihai He. "Adaptive Critic Design for Energy Minimization of Portable Video Communication Devices." IEEE Transactions on Circuits and Systems for Video Technology 20, no. 1 (January 2010): 27–37. http://dx.doi.org/10.1109/tcsvt.2009.2026835.

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32

Mu, Chaoxu, Ding Wang, Changyin Sun, and Qun Zong. "Robust adaptive critic control design with network-based event-triggered formulation." Nonlinear Dynamics 90, no. 3 (September 6, 2017): 2023–35. http://dx.doi.org/10.1007/s11071-017-3778-5.

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33

Liang, Mian Xin. "ADACD-Based Novel Optimal Model Identification Scheme for MIMO Discrete Nonlinear Systems." Applied Mechanics and Materials 397-400 (September 2013): 1006–9. http://dx.doi.org/10.4028/www.scientific.net/amm.397-400.1006.

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A model identification scheme based on the action dependent adaptive critic design (ADACD) is proposed for MIMO discrete nonlinear system. This scheme first introduces a critic network to approximate the overall identification evaluation of the system and then adjust the parameters of the identification network (i.e. action network) to minimize the output of the critic network. The system is proved to be uniformly ultimately bounded by using Lyapunov method. Furthermore, the weights of the critic and identification networks are also guaranteed to be bounded.
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34

Zhen Ni, Haibo He, and Jinyu Wen. "Adaptive Learning in Tracking Control Based on the Dual Critic Network Design." IEEE Transactions on Neural Networks and Learning Systems 24, no. 6 (June 2013): 913–28. http://dx.doi.org/10.1109/tnnls.2013.2247627.

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35

Ha, Mingming, Ding Wang, and Derong Liu. "Event-Triggered Adaptive Critic Control Design for Discrete-Time Constrained Nonlinear Systems." IEEE Transactions on Systems, Man, and Cybernetics: Systems 50, no. 9 (September 2020): 3158–68. http://dx.doi.org/10.1109/tsmc.2018.2868510.

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36

Wang, Ding, and Mingming Ha. "Mixed Driven Iterative Adaptive Critic Control Design Towards Nonaffine Discrete-Time Plants." IFAC-PapersOnLine 53, no. 2 (2020): 3803–8. http://dx.doi.org/10.1016/j.ifacol.2020.12.2071.

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37

Lian, Chuanqiang, Xin Xu, Lei Zuo, and Zhenhua Huang. "Adaptive critic design with graph Laplacian for online learning control of nonlinear systems." International Journal of Adaptive Control and Signal Processing 28, no. 3-5 (October 19, 2012): 290–304. http://dx.doi.org/10.1002/acs.2344.

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38

Tooranjipour, Pouria, and Ramin Vatankhah. "Adaptive critic-based quaternion neuro-fuzzy controller design with application to chaos control." Applied Soft Computing 70 (September 2018): 622–32. http://dx.doi.org/10.1016/j.asoc.2018.06.012.

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39

Wu, Ke, Qinmin Yang, Cheng Kang, Xin Zhang, and Zhiyi Huang. "Adaptive Critic Design Based Control of Tunnel Ventilation System with Variable Jet Speed." Journal of Signal Processing Systems 86, no. 2-3 (March 1, 2016): 269–78. http://dx.doi.org/10.1007/s11265-016-1123-8.

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40

Han, Junbiao, Sarika Khushalani-Solanki, Jignesh Solanki, and Jiaqi Liang. "Adaptive Critic Design-Based Dynamic Stochastic Optimal Control Design for a Microgrid With Multiple Renewable Resources." IEEE Transactions on Smart Grid 6, no. 6 (November 2015): 2694–703. http://dx.doi.org/10.1109/tsg.2015.2428435.

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41

Kumar, Swagat, Radhakant Padhi, and Laxmidhar Behera. "Continuous-Time Single Network Adaptive Critic for Regulator Design of Nonlinear Control Affine Systems." IFAC Proceedings Volumes 41, no. 2 (2008): 8797–802. http://dx.doi.org/10.3182/20080706-5-kr-1001.01487.

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42

Lin, C. K. "Adaptive Critic Autopilot Design of Bank-to-Turn Missiles Using Fuzzy Basis Function Networks." IEEE Transactions on Systems, Man and Cybernetics, Part B (Cybernetics) 35, no. 2 (April 2005): 197–207. http://dx.doi.org/10.1109/tsmcb.2004.842246.

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43

Bu, Xiangwei. "An improvement of single-network adaptive critic design for nonlinear systems with asymmetry constraints." Journal of the Franklin Institute 356, no. 16 (November 2019): 9646–64. http://dx.doi.org/10.1016/j.jfranklin.2019.09.021.

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44

Prasad, Lal Bahadur, Barjeev Tyagi, and Hari Om Gupta. "Adaptive Critic Design Using Policy Iteration Technique for LTI Systems: A Comprehensive Performance Analysis." Journal of Control, Automation and Electrical Systems 26, no. 2 (February 7, 2015): 134–48. http://dx.doi.org/10.1007/s40313-015-0167-5.

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45

Lin, Wei-Song, and Ping-Chieh Yang. "Adaptive critic motion control design of autonomous wheeled mobile robot by dual heuristic programming." Automatica 44, no. 11 (November 2008): 2716–23. http://dx.doi.org/10.1016/j.automatica.2008.03.029.

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46

Dutta, Oindrilla, and Ahmed Mohamed. "Reducing the risk of cascading failure in active distribution networks using adaptive critic design." IET Generation, Transmission & Distribution 14, no. 13 (July 3, 2020): 2592–601. http://dx.doi.org/10.1049/iet-gtd.2020.0045.

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47

Shafiekhani, A., M. J. Mahjoob, and M. Akraminia. "Design and implementation of an adaptive critic-based neuro-fuzzy controller on an unmanned bicycle." Mechatronics 28 (June 2015): 115–23. http://dx.doi.org/10.1016/j.mechatronics.2015.04.010.

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48

Hager, LvS, K. R. Uren, G. van Schoor, and A. Janse van Rensburg. "Adaptive Neural network control of a helicopter system with optimal observer and actor-critic design." Neurocomputing 302 (August 2018): 75–90. http://dx.doi.org/10.1016/j.neucom.2018.04.004.

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49

Bu, Xiangwei, Yu Xiao, and Humin Lei. "An Adaptive Critic Design-Based Fuzzy Neural Controller for Hypersonic Vehicles: Predefined Behavioral Nonaffine Control." IEEE/ASME Transactions on Mechatronics 24, no. 4 (August 2019): 1871–81. http://dx.doi.org/10.1109/tmech.2019.2928699.

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50

Wang, Ding, Chaoxu Mu, Derong Liu, and Hongwen Ma. "On Mixed Data and Event Driven Design for Adaptive-Critic-Based Nonlinear $H_{\infty}$ Control." IEEE Transactions on Neural Networks and Learning Systems 29, no. 4 (April 2018): 993–1005. http://dx.doi.org/10.1109/tnnls.2016.2642128.

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